Glossary of algebraic geometry

This is a glossary of algebraic geometry. ^[1]

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Table of Contents

1. 273 relations: Abelian variety, Adequate equivalence relation, Adjunction formula, Affine space, Affine variety, Algebraic closure, Algebraic curve, Algebraic cycle, Algebraic geometry, Algebraic group, Algebraic number field, Algebraic number theory, Algebraic space, Algebraic stack, Algebraic surface, Algebraic torus, Algebraic variety, Algebraically closed field, Ample line bundle, André Weil, Arakelov theory, Arithmetic and geometric Frobenius, Arithmetic genus, Artinian ring, Éléments de géométrie algébrique, Barsotti–Tate group, Base change theorems, Behrend function, Behrend's trace formula, Berkovich space, Birational geometry, Blowing up, Borel subgroup, Calabi–Yau manifold, Canonical bundle, Canonical ring, Canonical singularity, Castelnuovo–Mumford regularity, Catenary ring, Chern class, Chow group, Classification theorem, Classifying space, Closed immersion, Cohen–Macaulay ring, Coherent duality, Coherent sheaf, Commutative ring, Commutative ring spectrum, Compact space, ... Expand index (223 more) » « Shrink index

2. Glossaries of mathematics
3. Scheme theory

Abelian variety

In mathematics, particularly in algebraic geometry, complex analysis and algebraic number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law that can be defined by regular functions.

See Glossary of algebraic geometry and Abelian variety

Adequate equivalence relation

In algebraic geometry, a branch of mathematics, an adequate equivalence relation is an equivalence relation on algebraic cycles of smooth projective varieties used to obtain a well-working theory of such cycles, and in particular, well-defined intersection products. Glossary of algebraic geometry and adequate equivalence relation are algebraic geometry.

See Glossary of algebraic geometry and Adequate equivalence relation

Adjunction formula

In mathematics, especially in algebraic geometry and the theory of complex manifolds, the adjunction formula relates the canonical bundle of a variety and a hypersurface inside that variety. Glossary of algebraic geometry and adjunction formula are algebraic geometry.

See Glossary of algebraic geometry and Adjunction formula

Affine space

In mathematics, an affine space is a geometric structure that generalizes some of the properties of Euclidean spaces in such a way that these are independent of the concepts of distance and measure of angles, keeping only the properties related to parallelism and ratio of lengths for parallel line segments.

See Glossary of algebraic geometry and Affine space

Affine variety

In algebraic geometry, an affine algebraic set is the set of the common zeros over an algebraically closed field of some family of polynomials in the polynomial ring k. An affine variety or affine algebraic variety, is an affine algebraic set such that the ideal generated by the defining polynomials is prime. Glossary of algebraic geometry and affine variety are algebraic geometry.

See Glossary of algebraic geometry and Affine variety

Algebraic closure

In mathematics, particularly abstract algebra, an algebraic closure of a field K is an algebraic extension of K that is algebraically closed.

See Glossary of algebraic geometry and Algebraic closure

Algebraic curve

In mathematics, an affine algebraic plane curve is the zero set of a polynomial in two variables.

See Glossary of algebraic geometry and Algebraic curve

Algebraic cycle

In mathematics, an algebraic cycle on an algebraic variety V is a formal linear combination of subvarieties of V. These are the part of the algebraic topology of V that is directly accessible by algebraic methods. Glossary of algebraic geometry and algebraic cycle are algebraic geometry.

See Glossary of algebraic geometry and Algebraic cycle

Algebraic geometry

Algebraic geometry is a branch of mathematics which uses abstract algebraic techniques, mainly from commutative algebra, to solve geometrical problems.

See Glossary of algebraic geometry and Algebraic geometry

Algebraic group

In mathematics, an algebraic group is an algebraic variety endowed with a group structure that is compatible with its structure as an algebraic variety.

See Glossary of algebraic geometry and Algebraic group

Algebraic number field

In mathematics, an algebraic number field (or simply number field) is an extension field K of the field of rational numbers such that the field extension K / \mathbb has finite degree (and hence is an algebraic field extension).

See Glossary of algebraic geometry and Algebraic number field

Algebraic number theory

Algebraic number theory is a branch of number theory that uses the techniques of abstract algebra to study the integers, rational numbers, and their generalizations.

See Glossary of algebraic geometry and Algebraic number theory

Algebraic space

In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by Michael Artin for use in deformation theory. Glossary of algebraic geometry and algebraic space are algebraic geometry.

See Glossary of algebraic geometry and Algebraic space

Algebraic stack

In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Glossary of algebraic geometry and algebraic stack are algebraic geometry.

See Glossary of algebraic geometry and Algebraic stack

Algebraic surface

In mathematics, an algebraic surface is an algebraic variety of dimension two.

See Glossary of algebraic geometry and Algebraic surface

Algebraic torus

In mathematics, an algebraic torus, where a one dimensional torus is typically denoted by \mathbf G_, \mathbb_m, or \mathbb, is a type of commutative affine algebraic group commonly found in projective algebraic geometry and toric geometry.

See Glossary of algebraic geometry and Algebraic torus

Algebraic variety

Algebraic varieties are the central objects of study in algebraic geometry, a sub-field of mathematics. Glossary of algebraic geometry and algebraic variety are algebraic geometry.

See Glossary of algebraic geometry and Algebraic variety

Algebraically closed field

In mathematics, a field is algebraically closed if every non-constant polynomial in (the univariate polynomial ring with coefficients in) has a root in.

See Glossary of algebraic geometry and Algebraically closed field

Ample line bundle

In mathematics, a distinctive feature of algebraic geometry is that some line bundles on a projective variety can be considered "positive", while others are "negative" (or a mixture of the two). Glossary of algebraic geometry and Ample line bundle are algebraic geometry.

See Glossary of algebraic geometry and Ample line bundle

André Weil

André Weil (6 May 1906 – 6 August 1998) was a French mathematician, known for his foundational work in number theory and algebraic geometry.

See Glossary of algebraic geometry and André Weil

Arakelov theory

In mathematics, Arakelov theory (or Arakelov geometry) is an approach to Diophantine geometry, named for Suren Arakelov. Glossary of algebraic geometry and Arakelov theory are algebraic geometry.

See Glossary of algebraic geometry and Arakelov theory

Arithmetic and geometric Frobenius

In mathematics, the Frobenius endomorphism is defined in any commutative ring R that has characteristic p, where p is a prime number. Glossary of algebraic geometry and Arithmetic and geometric Frobenius are algebraic geometry.

See Glossary of algebraic geometry and Arithmetic and geometric Frobenius

Arithmetic genus

In mathematics, the arithmetic genus of an algebraic variety is one of a few possible generalizations of the genus of an algebraic curve or Riemann surface.

See Glossary of algebraic geometry and Arithmetic genus

Artinian ring

In mathematics, specifically abstract algebra, an Artinian ring (sometimes Artin ring) is a ring that satisfies the descending chain condition on (one-sided) ideals; that is, there is no infinite descending sequence of ideals.

See Glossary of algebraic geometry and Artinian ring

Éléments de géométrie algébrique

The Éléments de géométrie algébrique ("Elements of Algebraic Geometry") by Alexander Grothendieck (assisted by Jean Dieudonné), or EGA for short, is a rigorous treatise, in French, on algebraic geometry that was published (in eight parts or fascicles) from 1960 through 1967 by the Institut des Hautes Études Scientifiques. Glossary of algebraic geometry and Éléments de géométrie algébrique are scheme theory.

See Glossary of algebraic geometry and Éléments de géométrie algébrique

Barsotti–Tate group

In algebraic geometry, Barsotti–Tate groups or p-divisible groups are similar to the points of order a power of p on an abelian variety in characteristic p. They were introduced by under the name equidimensional hyperdomain and by under the name p-divisible groups, and named Barsotti–Tate groups by.

See Glossary of algebraic geometry and Barsotti–Tate group

Base change theorems

In mathematics, the base change theorems relate the direct image and the inverse image of sheaves.

See Glossary of algebraic geometry and Base change theorems

Behrend function

In algebraic geometry, the Behrend function of a scheme X, introduced by Kai Behrend, is a constructible function such that if X is a quasi-projective proper moduli scheme carrying a symmetric obstruction theory, then the weighted Euler characteristic is the degree of the virtual fundamental class of X, which is an element of the zeroth Chow group of X.

See Glossary of algebraic geometry and Behrend function

Behrend's trace formula

In algebraic geometry, Behrend's trace formula is a generalization of the Grothendieck–Lefschetz trace formula to a smooth algebraic stack over a finite field conjectured in 1993 and proven in 2003 by Kai Behrend.

See Glossary of algebraic geometry and Behrend's trace formula

Berkovich space

In mathematics, a Berkovich space, introduced by, is a version of an analytic space over a non-Archimedean field (e.g. ''p''-adic field), refining Tate's notion of a rigid analytic space. Glossary of algebraic geometry and Berkovich space are algebraic geometry.

See Glossary of algebraic geometry and Berkovich space

Birational geometry

In mathematics, birational geometry is a field of algebraic geometry in which the goal is to determine when two algebraic varieties are isomorphic outside lower-dimensional subsets. Glossary of algebraic geometry and birational geometry are algebraic geometry.

See Glossary of algebraic geometry and Birational geometry

Blowing up

In mathematics, blowing up or blowup is a type of geometric transformation which replaces a subspace of a given space with the space of all directions pointing out of that subspace.

See Glossary of algebraic geometry and Blowing up

Borel subgroup

In the theory of algebraic groups, a Borel subgroup of an algebraic group G is a maximal Zariski closed and connected solvable algebraic subgroup.

See Glossary of algebraic geometry and Borel subgroup

Calabi–Yau manifold

In algebraic and differential geometry, a Calabi–Yau manifold, also known as a Calabi–Yau space, is a particular type of manifold which has properties, such as Ricci flatness, yielding applications in theoretical physics. Glossary of algebraic geometry and Calabi–Yau manifold are algebraic geometry.

See Glossary of algebraic geometry and Calabi–Yau manifold

Canonical bundle

In mathematics, the canonical bundle of a non-singular algebraic variety V of dimension n over a field is the line bundle \,\!\Omega^n.

See Glossary of algebraic geometry and Canonical bundle

Canonical ring

In mathematics, the pluricanonical ring of an algebraic variety V (which is nonsingular), or of a complex manifold, is the graded ring of sections of powers of the canonical bundle K. Its nth graded component (for n\geq 0) is: that is, the space of sections of the n-th tensor product Kn of the canonical bundle K. Glossary of algebraic geometry and canonical ring are algebraic geometry.

See Glossary of algebraic geometry and Canonical ring

Canonical singularity

In mathematics, canonical singularities appear as singularities of the canonical model of a projective variety, and terminal singularities are special cases that appear as singularities of minimal models. Glossary of algebraic geometry and canonical singularity are algebraic geometry.

See Glossary of algebraic geometry and Canonical singularity

Castelnuovo–Mumford regularity

In algebraic geometry, the Castelnuovo–Mumford regularity of a coherent sheaf F over projective space \mathbf^n is the smallest integer r such that it is r-regular, meaning that whenever i>0. Glossary of algebraic geometry and Castelnuovo–Mumford regularity are algebraic geometry.

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Catenary ring

In mathematics, a commutative ring R is catenary if for any pair of prime ideals p, q, any two strictly increasing chains of prime ideals are contained in maximal strictly increasing chains from p to q of the same (finite) length. Glossary of algebraic geometry and catenary ring are algebraic geometry.

See Glossary of algebraic geometry and Catenary ring

Chern class

In mathematics, in particular in algebraic topology, differential geometry and algebraic geometry, the Chern classes are characteristic classes associated with complex vector bundles.

See Glossary of algebraic geometry and Chern class

Chow group

In algebraic geometry, the Chow groups (named after Wei-Liang Chow by) of an algebraic variety over any field are algebro-geometric analogs of the homology of a topological space. Glossary of algebraic geometry and Chow group are algebraic geometry.

See Glossary of algebraic geometry and Chow group

Classification theorem

In mathematics, a classification theorem answers the classification problem: "What are the objects of a given type, up to some equivalence?".

See Glossary of algebraic geometry and Classification theorem

Classifying space

In mathematics, specifically in homotopy theory, a classifying space BG of a topological group G is the quotient of a weakly contractible space EG (i.e., a topological space all of whose homotopy groups are trivial) by a proper free action of G. It has the property that any G principal bundle over a paracompact manifold is isomorphic to a pullback of the principal bundle EG \to BG.

See Glossary of algebraic geometry and Classifying space

Closed immersion

In algebraic geometry, a closed immersion of schemes is a morphism of schemes f: Z \to X that identifies Z as a closed subset of X such that locally, regular functions on Z can be extended to X. The latter condition can be formalized by saying that f^\#:\mathcal_X\rightarrow f_\ast\mathcal_Z is surjective.

See Glossary of algebraic geometry and Closed immersion

Cohen–Macaulay ring

In mathematics, a Cohen–Macaulay ring is a commutative ring with some of the algebro-geometric properties of a smooth variety, such as local equidimensionality. Glossary of algebraic geometry and Cohen–Macaulay ring are algebraic geometry.

See Glossary of algebraic geometry and Cohen–Macaulay ring

Coherent duality

In mathematics, coherent duality is any of a number of generalisations of Serre duality, applying to coherent sheaves, in algebraic geometry and complex manifold theory, as well as some aspects of commutative algebra that are part of the 'local' theory.

See Glossary of algebraic geometry and Coherent duality

Coherent sheaf

In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaves are a class of sheaves closely linked to the geometric properties of the underlying space. Glossary of algebraic geometry and coherent sheaf are algebraic geometry.

See Glossary of algebraic geometry and Coherent sheaf

Commutative ring

In mathematics, a commutative ring is a ring in which the multiplication operation is commutative.

See Glossary of algebraic geometry and Commutative ring

Commutative ring spectrum

In algebraic topology, a commutative ring spectrum, roughly equivalent to a E_\infty-ring spectrum, is a commutative monoid in a good category of spectra.

See Glossary of algebraic geometry and Commutative ring spectrum

Compact space

In mathematics, specifically general topology, compactness is a property that seeks to generalize the notion of a closed and bounded subset of Euclidean space.

See Glossary of algebraic geometry and Compact space

Complete intersection ring

In commutative algebra, a complete intersection ring is a commutative ring similar to the coordinate rings of varieties that are complete intersections.

See Glossary of algebraic geometry and Complete intersection ring

Complete set of invariants

In mathematics, a complete set of invariants for a classification problem is a collection of maps (where X is the collection of objects being classified, up to some equivalence relation \sim, and the Y_i are some sets), such that x \sim x' if and only if f_i(x).

See Glossary of algebraic geometry and Complete set of invariants

Complete variety

In mathematics, in particular in algebraic geometry, a complete algebraic variety is an algebraic variety, such that for any variety the projection morphism is a closed map (i.e. maps closed sets onto closed sets).

See Glossary of algebraic geometry and Complete variety

Complex manifold

In differential geometry and complex geometry, a complex manifold is a manifold with an atlas of charts to the open unit disc in the complex coordinate space \mathbb^n, such that the transition maps are holomorphic.

See Glossary of algebraic geometry and Complex manifold

Composition series

In abstract algebra, a composition series provides a way to break up an algebraic structure, such as a group or a module, into simple pieces.

See Glossary of algebraic geometry and Composition series

Connected space

In topology and related branches of mathematics, a connected space is a topological space that cannot be represented as the union of two or more disjoint non-empty open subsets.

See Glossary of algebraic geometry and Connected space

Convex cone

In linear algebra, a cone—sometimes called a linear cone for distinguishing it from other sorts of cones—is a subset of a vector space that is closed under positive scalar multiplication; that is, is a cone if x\in C implies sx\in C for every.

See Glossary of algebraic geometry and Convex cone

Cotangent sheaf

In algebraic geometry, given a morphism f: X → S of schemes, the cotangent sheaf on X is the sheaf of \mathcalO_X-modules \Omega_ that represents (or classifies) S-derivations in the sense: for any \mathcal_X-modules F, there is an isomorphism that depends naturally on F. In other words, the cotangent sheaf is characterized by the universal property: there is the differential d: \mathcal_X \to \Omega_ such that any S-derivation D: \mathcal_X \to F factors as D. Glossary of algebraic geometry and cotangent sheaf are algebraic geometry.

See Glossary of algebraic geometry and Cotangent sheaf

Cox ring

In algebraic geometry, a Cox ring is a sort of universal homogeneous coordinate ring for a projective variety, and is (roughly speaking) a direct sum of the spaces of sections of all isomorphism classes of line bundles. Glossary of algebraic geometry and cox ring are algebraic geometry.

See Glossary of algebraic geometry and Cox ring

Crepant resolution

In algebraic geometry, a crepant resolution of a singularity is a resolution that does not affect the canonical class of the manifold. Glossary of algebraic geometry and crepant resolution are algebraic geometry.

See Glossary of algebraic geometry and Crepant resolution

Deformation (mathematics)

In mathematics, deformation theory is the study of infinitesimal conditions associated with varying a solution P of a problem to slightly different solutions Pε, where ε is a small number, or a vector of small quantities. Glossary of algebraic geometry and deformation (mathematics) are algebraic geometry.

See Glossary of algebraic geometry and Deformation (mathematics)

Degeneration (algebraic geometry)

In algebraic geometry, a degeneration (or specialization) is the act of taking a limit of a family of varieties. Glossary of algebraic geometry and degeneration (algebraic geometry) are algebraic geometry.

See Glossary of algebraic geometry and Degeneration (algebraic geometry)

Degree of a field extension

In mathematics, more specifically field theory, the degree of a field extension is a rough measure of the "size" of the field extension.

See Glossary of algebraic geometry and Degree of a field extension

Degree of an algebraic variety

In mathematics, the degree of an affine or projective variety of dimension is the number of intersection points of the variety with hyperplanes in general position.

See Glossary of algebraic geometry and Degree of an algebraic variety

Deligne–Mumford stack

In algebraic geometry, a Deligne–Mumford stack is a stack F such that Pierre Deligne and David Mumford introduced this notion in 1969 when they proved that moduli spaces of stable curves of fixed arithmetic genus are proper smooth Deligne–Mumford stacks. Glossary of algebraic geometry and Deligne–Mumford stack are algebraic geometry.

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Dense set

In topology and related areas of mathematics, a subset A of a topological space X is said to be dense in X if every point of X either belongs to A or else is arbitrarily "close" to a member of A — for instance, the rational numbers are a dense subset of the real numbers because every real number either is a rational number or has a rational number arbitrarily close to it (see Diophantine approximation).

See Glossary of algebraic geometry and Dense set

Derived algebraic geometry

Derived algebraic geometry is a branch of mathematics that generalizes algebraic geometry to a situation where commutative rings, which provide local charts, are replaced by either differential graded algebras (over \mathbb), simplicial commutative rings or E_\infty-ring spectra from algebraic topology, whose higher homotopy groups account for the non-discreteness (e.g., Tor) of the structure sheaf. Glossary of algebraic geometry and Derived algebraic geometry are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Derived algebraic geometry

Diagonal

In geometry, a diagonal is a line segment joining two vertices of a polygon or polyhedron, when those vertices are not on the same edge.

See Glossary of algebraic geometry and Diagonal

Diagonal morphism (algebraic geometry)

In algebraic geometry, given a morphism of schemes p: X \to S, the diagonal morphism is a morphism determined by the universal property of the fiber product X \times_S X of p and p applied to the identity 1_X: X \to X and the identity 1_X. Glossary of algebraic geometry and diagonal morphism (algebraic geometry) are algebraic geometry.

See Glossary of algebraic geometry and Diagonal morphism (algebraic geometry)

Dimension of a scheme

In algebraic geometry, the dimension of a scheme is a generalization of a dimension of an algebraic variety. Glossary of algebraic geometry and dimension of a scheme are algebraic geometry.

See Glossary of algebraic geometry and Dimension of a scheme

Dimension of an algebraic variety

In mathematics and specifically in algebraic geometry, the dimension of an algebraic variety may be defined in various equivalent ways.

See Glossary of algebraic geometry and Dimension of an algebraic variety

Disjoint union

In mathematics, the disjoint union (or discriminated union) A \sqcup B of the sets and is the set formed from the elements of and labelled (indexed) with the name of the set from which they come.

See Glossary of algebraic geometry and Disjoint union

Divisor (algebraic geometry)

In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties.

See Glossary of algebraic geometry and Divisor (algebraic geometry)

Divisorial scheme

In algebraic geometry, a divisorial scheme is a scheme admitting an ample family of line bundles, as opposed to an ample line bundle. Glossary of algebraic geometry and divisorial scheme are algebraic geometry.

See Glossary of algebraic geometry and Divisorial scheme

Dualizing sheaf

In algebraic geometry, the dualizing sheaf on a proper scheme X of dimension n over a field k is a coherent sheaf \omega_X together with a linear functional that induces a natural isomorphism of vector spaces for each coherent sheaf F on X (the superscript * refers to a dual vector space). Glossary of algebraic geometry and dualizing sheaf are algebraic geometry.

See Glossary of algebraic geometry and Dualizing sheaf

Elliptic curve

In mathematics, an elliptic curve is a smooth, projective, algebraic curve of genus one, on which there is a specified point.

See Glossary of algebraic geometry and Elliptic curve

Enriques–Kodaira classification

In mathematics, the Enriques–Kodaira classification groups compact complex surfaces into ten classes, each parametrized by a moduli space.

See Glossary of algebraic geometry and Enriques–Kodaira classification

Equivariant sheaf

In mathematics, given an action \sigma: G \times_S X \to X of a group scheme G on a scheme X over a base scheme S, an equivariant sheaf F on X is a sheaf of \mathcalO_X-modules together with the isomorphism of \mathcal_-modules that satisfies the cocycle condition: writing m for multiplication,. Glossary of algebraic geometry and equivariant sheaf are scheme theory.

See Glossary of algebraic geometry and Equivariant sheaf

Euler characteristic

In mathematics, and more specifically in algebraic topology and polyhedral combinatorics, the Euler characteristic (or Euler number, or Euler–Poincaré characteristic) is a topological invariant, a number that describes a topological space's shape or structure regardless of the way it is bent.

See Glossary of algebraic geometry and Euler characteristic

Euler sequence

In mathematics, the Euler sequence is a particular exact sequence of sheaves on n-dimensional projective space over a ring. Glossary of algebraic geometry and Euler sequence are algebraic geometry.

See Glossary of algebraic geometry and Euler sequence

Fano variety

In algebraic geometry, a Fano variety, introduced by Gino Fano in, is an algebraic variety that generalizes certain aspects of complete intersections of algebraic hypersurfaces whose sum of degrees is at most the total dimension of the ambient projective space. Glossary of algebraic geometry and Fano variety are algebraic geometry.

See Glossary of algebraic geometry and Fano variety

Field (mathematics)

In mathematics, a field is a set on which addition, subtraction, multiplication, and division are defined and behave as the corresponding operations on rational and real numbers.

See Glossary of algebraic geometry and Field (mathematics)

Field with one element

In mathematics, the field with one element is a suggestive name for an object that should behave similarly to a finite field with a single element, if such a field could exist. Glossary of algebraic geometry and field with one element are algebraic geometry.

See Glossary of algebraic geometry and Field with one element

Finite morphism

In algebraic geometry, a finite morphism between two affine varieties X, Y is a dense regular map which induces isomorphic inclusion k\left\hookrightarrow k\left between their coordinate rings, such that k\left is integral over k\left. Glossary of algebraic geometry and finite morphism are algebraic geometry.

See Glossary of algebraic geometry and Finite morphism

Flag (linear algebra)

In mathematics, particularly in linear algebra, a flag is an increasing sequence of subspaces of a finite-dimensional vector space V. Here "increasing" means each is a proper subspace of the next (see filtration): The term flag is motivated by a particular example resembling a flag: the zero point, a line, and a plane correspond to a nail, a staff, and a sheet of fabric.

See Glossary of algebraic geometry and Flag (linear algebra)

Flat module

In algebra, flat modules include free modules, projective modules, and, over a principal ideal domain, torsion free modules. Glossary of algebraic geometry and flat module are algebraic geometry.

See Glossary of algebraic geometry and Flat module

Flat morphism

In mathematics, in particular in the theory of schemes in algebraic geometry, a flat morphism f from a scheme X to a scheme Y is a morphism such that the induced map on every stalk is a flat map of rings, i.e., is a flat map for all P in X. A map of rings A\to B is called flat if it is a homomorphism that makes B a flat A-module.

See Glossary of algebraic geometry and Flat morphism

Formal scheme

In mathematics, specifically in algebraic geometry, a formal scheme is a type of space which includes data about its surroundings. Glossary of algebraic geometry and formal scheme are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Formal scheme

Frobenius endomorphism

In commutative algebra and field theory, the Frobenius endomorphism (after Ferdinand Georg Frobenius) is a special endomorphism of commutative rings with prime characteristic, an important class that includes finite fields.

See Glossary of algebraic geometry and Frobenius endomorphism

Function field (scheme theory)

The sheaf of rational functions KX of a scheme X is the generalization to scheme theory of the notion of function field of an algebraic variety in classical algebraic geometry. Glossary of algebraic geometry and function field (scheme theory) are scheme theory.

See Glossary of algebraic geometry and Function field (scheme theory)

Function field of an algebraic variety

In algebraic geometry, the function field of an algebraic variety V consists of objects that are interpreted as rational functions on V. In classical algebraic geometry they are ratios of polynomials; in complex geometry these are meromorphic functions and their higher-dimensional analogues; in modern algebraic geometry they are elements of some quotient ring's field of fractions.

See Glossary of algebraic geometry and Function field of an algebraic variety

Gabriel–Rosenberg reconstruction theorem

In algebraic geometry, the Gabriel–Rosenberg reconstruction theorem, introduced in, states that a quasi-separated scheme can be recovered from the category of quasi-coherent sheaves on it. Glossary of algebraic geometry and Gabriel–Rosenberg reconstruction theorem are scheme theory.

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Generalized flag variety

In mathematics, a generalized flag variety (or simply flag variety) is a homogeneous space whose points are flags in a finite-dimensional vector space V over a field F. When F is the real or complex numbers, a generalized flag variety is a smooth or complex manifold, called a real or complex flag manifold.

See Glossary of algebraic geometry and Generalized flag variety

Generic point

In algebraic geometry, a generic point P of an algebraic variety X is a point in a general position, at which all generic properties are true, a generic property being a property which is true for almost every point. Glossary of algebraic geometry and generic point are algebraic geometry.

See Glossary of algebraic geometry and Generic point

Genus–degree formula

In classical algebraic geometry, the genus–degree formula relates the degree d of an irreducible plane curve C with its arithmetic genus g via the formula: Here "plane curve" means that C is a closed curve in the projective plane \mathbb^2.

See Glossary of algebraic geometry and Genus–degree formula

Geometric genus

In algebraic geometry, the geometric genus is a basic birational invariant of algebraic varieties and complex manifolds.

See Glossary of algebraic geometry and Geometric genus

Geometric quotient

In algebraic geometry, a geometric quotient of an algebraic variety X with the action of an algebraic group G is a morphism of varieties \pi: X \to Y such that The notion appears in geometric invariant theory. Glossary of algebraic geometry and geometric quotient are algebraic geometry.

See Glossary of algebraic geometry and Geometric quotient

Geometrically (algebraic geometry)

In algebraic geometry, especially in scheme theory, a property is said to hold geometrically over a field if it also holds over the algebraic closure of the field. Glossary of algebraic geometry and geometrically (algebraic geometry) are scheme theory.

See Glossary of algebraic geometry and Geometrically (algebraic geometry)

Gerbe

In mathematics, a gerbe is a construct in homological algebra and topology.

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GIT quotient

In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme X. Glossary of algebraic geometry and GIT quotient are algebraic geometry.

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Global dimension

In ring theory and homological algebra, the global dimension (or global homological dimension; sometimes just called homological dimension) of a ring A denoted gl dim A, is a non-negative integer or infinity which is a homological invariant of the ring.

See Glossary of algebraic geometry and Global dimension

Glossary of algebraic geometry

This is a glossary of algebraic geometry. Glossary of algebraic geometry and glossary of algebraic geometry are algebraic geometry, Glossaries of mathematics and scheme theory.

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Glossary of arithmetic and diophantine geometry

This is a glossary of arithmetic and diophantine geometry in mathematics, areas growing out of the traditional study of Diophantine equations to encompass large parts of number theory and algebraic geometry. Glossary of algebraic geometry and glossary of arithmetic and diophantine geometry are algebraic geometry and Glossaries of mathematics.

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Glossary of classical algebraic geometry

The terminology of algebraic geometry changed drastically during the twentieth century, with the introduction of the general methods, initiated by David Hilbert and the Italian school of algebraic geometry in the beginning of the century, and later formalized by André Weil, Jean-Pierre Serre and Alexander Grothendieck. Glossary of algebraic geometry and Glossary of classical algebraic geometry are algebraic geometry and Glossaries of mathematics.

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Glossary of commutative algebra

This is a glossary of commutative algebra. Glossary of algebraic geometry and glossary of commutative algebra are Glossaries of mathematics.

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Glossary of differential geometry and topology

This is a glossary of terms specific to differential geometry and differential topology. Glossary of algebraic geometry and glossary of differential geometry and topology are Glossaries of mathematics.

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Glossary of Riemannian and metric geometry

This is a glossary of some terms used in Riemannian geometry and metric geometry — it doesn't cover the terminology of differential topology. Glossary of algebraic geometry and glossary of Riemannian and metric geometry are Glossaries of mathematics.

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Glossary of ring theory

Ring theory is the branch of mathematics in which rings are studied: that is, structures supporting both an addition and a multiplication operation. Glossary of algebraic geometry and Glossary of ring theory are Glossaries of mathematics.

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Gorenstein ring

In commutative algebra, a Gorenstein local ring is a commutative Noetherian local ring R with finite injective dimension as an ''R''-module.

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Gorenstein scheme

In algebraic geometry, a Gorenstein scheme is a locally Noetherian scheme whose local rings are all Gorenstein. Glossary of algebraic geometry and Gorenstein scheme are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Gorenstein scheme

Grassmannian

In mathematics, the Grassmannian \mathbf_k(V) (named in honour of Hermann Grassmann) is a differentiable manifold that parameterizes the set of all k-dimensional linear subspaces of an n-dimensional vector space V over a field K. For example, the Grassmannian \mathbf_1(V) is the space of lines through the origin in V, so it is the same as the projective space \mathbf(V) of one dimension lower than V. Glossary of algebraic geometry and Grassmannian are algebraic geometry.

See Glossary of algebraic geometry and Grassmannian

Grauert–Riemenschneider vanishing theorem

In mathematics, the Grauert–Riemenschneider vanishing theorem is an extension of the Kodaira vanishing theorem on the vanishing of higher cohomology groups of coherent sheaves on a compact complex manifold, due to.

See Glossary of algebraic geometry and Grauert–Riemenschneider vanishing theorem

Grothendieck trace formula

In algebraic geometry, the Grothendieck trace formula expresses the number of points of a variety over a finite field in terms of the trace of the Frobenius endomorphism on its cohomology groups.

See Glossary of algebraic geometry and Grothendieck trace formula

Grothendieck's relative point of view

Grothendieck's relative point of view is a heuristic applied in certain abstract mathematical situations, with a rough meaning of taking for consideration families of 'objects' explicitly depending on parameters, as the basic field of study, rather than a single such object. Glossary of algebraic geometry and Grothendieck's relative point of view are scheme theory.

See Glossary of algebraic geometry and Grothendieck's relative point of view

Grothendieck–Riemann–Roch theorem

In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology.

See Glossary of algebraic geometry and Grothendieck–Riemann–Roch theorem

Group (mathematics)

In mathematics, a group is a set with an operation that associates an element of the set to every pair of elements of the set (as does every binary operation) and satisfies the following constraints: the operation is associative, it has an identity element, and every element of the set has an inverse element.

See Glossary of algebraic geometry and Group (mathematics)

Group scheme

In mathematics, a group scheme is a type of object from algebraic geometry equipped with a composition law. Glossary of algebraic geometry and group scheme are scheme theory.

See Glossary of algebraic geometry and Group scheme

Group-scheme action

In algebraic geometry, an action of a group scheme is a generalization of a group action to a group scheme. Glossary of algebraic geometry and group-scheme action are algebraic geometry.

See Glossary of algebraic geometry and Group-scheme action

Hilbert series and Hilbert polynomial

In commutative algebra, the Hilbert function, the Hilbert polynomial, and the Hilbert series of a graded commutative algebra finitely generated over a field are three strongly related notions which measure the growth of the dimension of the homogeneous components of the algebra. Glossary of algebraic geometry and Hilbert series and Hilbert polynomial are algebraic geometry.

See Glossary of algebraic geometry and Hilbert series and Hilbert polynomial

Hodge bundle

In mathematics, the Hodge bundle, named after W. V. D. Hodge, appears in the study of families of curves, where it provides an invariant in the moduli theory of algebraic curves.

See Glossary of algebraic geometry and Hodge bundle

Hodge theory

In mathematics, Hodge theory, named after W. V. D. Hodge, is a method for studying the cohomology groups of a smooth manifold M using partial differential equations.

See Glossary of algebraic geometry and Hodge theory

Homogeneous coordinate ring

In algebraic geometry, the homogeneous coordinate ring R of an algebraic variety V given as a subvariety of projective space of a given dimension N is by definition the quotient ring where I is the homogeneous ideal defining V, K is the algebraically closed field over which V is defined, and is the polynomial ring in N + 1 variables Xi.

See Glossary of algebraic geometry and Homogeneous coordinate ring

Hyperconnected space

In the mathematical field of topology, a hyperconnected space or irreducible space is a topological space X that cannot be written as the union of two proper closed subsets (whether disjoint or non-disjoint).

See Glossary of algebraic geometry and Hyperconnected space

Hyperelliptic curve

In algebraic geometry, a hyperelliptic curve is an algebraic curve of genus g > 1, given by an equation of the form y^2 + h(x)y.

See Glossary of algebraic geometry and Hyperelliptic curve

Ideal sheaf

In algebraic geometry and other areas of mathematics, an ideal sheaf (or sheaf of ideals) is the global analogue of an ideal in a ring. Glossary of algebraic geometry and ideal sheaf are scheme theory.

See Glossary of algebraic geometry and Ideal sheaf

Idempotence

Idempotence is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result beyond the initial application.

See Glossary of algebraic geometry and Idempotence

If and only if

In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") is paraphrased by the biconditional, a logical connective between statements.

See Glossary of algebraic geometry and If and only if

Iitaka dimension

In algebraic geometry, the Iitaka dimension of a line bundle L on an algebraic variety X is the dimension of the image of the rational map to projective space determined by L. This is 1 less than the dimension of the section ring of L The Iitaka dimension of L is always less than or equal to the dimension of X.

See Glossary of algebraic geometry and Iitaka dimension

Image (mathematics)

In mathematics, for a function f: X \to Y, the image of an input value x is the single output value produced by f when passed x. The preimage of an output value y is the set of input values that produce y. More generally, evaluating f at each element of a given subset A of its domain X produces a set, called the "image of A under (or through) f".

See Glossary of algebraic geometry and Image (mathematics)

Ind-scheme

In algebraic geometry, an ind-scheme is a set-valued functor that can be written (represented) as a direct limit (i.e., inductive limit) of closed embedding of schemes. Glossary of algebraic geometry and ind-scheme are algebraic geometry.

See Glossary of algebraic geometry and Ind-scheme

Initial and terminal objects

In category theory, a branch of mathematics, an initial object of a category is an object in such that for every object in, there exists precisely one morphism.

See Glossary of algebraic geometry and Initial and terminal objects

Integer

An integer is the number zero (0), a positive natural number (1, 2, 3,...), or the negation of a positive natural number (−1, −2, −3,...). The negations or additive inverses of the positive natural numbers are referred to as negative integers.

See Glossary of algebraic geometry and Integer

Integral domain

In mathematics, an integral domain is a nonzero commutative ring in which the product of any two nonzero elements is nonzero.

See Glossary of algebraic geometry and Integral domain

Integrally closed domain

In commutative algebra, an integrally closed domain A is an integral domain whose integral closure in its field of fractions is A itself.

See Glossary of algebraic geometry and Integrally closed domain

Integration along fibers

In differential geometry, the integration along fibers of a ''k''-form yields a (k-m)-form where m is the dimension of the fiber, via "integration".

See Glossary of algebraic geometry and Integration along fibers

Irreducible component

In algebraic geometry, an irreducible algebraic set or irreducible variety is an algebraic set that cannot be written as the union of two proper algebraic subsets. Glossary of algebraic geometry and irreducible component are algebraic geometry.

See Glossary of algebraic geometry and Irreducible component

Irreducible polynomial

In mathematics, an irreducible polynomial is, roughly speaking, a polynomial that cannot be factored into the product of two non-constant polynomials.

See Glossary of algebraic geometry and Irreducible polynomial

Irreducible ring

In mathematics, especially in the field of ring theory, the term irreducible ring is used in a few different ways.

See Glossary of algebraic geometry and Irreducible ring

Jacobian variety

In mathematics, the Jacobian variety J(C) of a non-singular algebraic curve C of genus g is the moduli space of degree 0 line bundles.

See Glossary of algebraic geometry and Jacobian variety

János Kollár

János Kollár (born 7 June 1956) is a Hungarian mathematician, specializing in algebraic geometry.

See Glossary of algebraic geometry and János Kollár

Kähler differential

In mathematics, Kähler differentials provide an adaptation of differential forms to arbitrary commutative rings or schemes. Glossary of algebraic geometry and Kähler differential are algebraic geometry.

See Glossary of algebraic geometry and Kähler differential

Kempf vanishing theorem

In algebraic geometry, the Kempf vanishing theorem, introduced by, states that the higher cohomology group Hi(G/B,L(λ)) (i > 0) vanishes whenever λ is a dominant weight of B.

See Glossary of algebraic geometry and Kempf vanishing theorem

Kodaira dimension

In algebraic geometry, the Kodaira dimension κ(X) measures the size of the canonical model of a projective variety X.

See Glossary of algebraic geometry and Kodaira dimension

Kodaira vanishing theorem

In mathematics, the Kodaira vanishing theorem is a basic result of complex manifold theory and complex algebraic geometry, describing general conditions under which sheaf cohomology groups with indices q > 0 are automatically zero.

See Glossary of algebraic geometry and Kodaira vanishing theorem

Kodaira–Spencer map

In mathematics, the Kodaira–Spencer map, introduced by Kunihiko Kodaira and Donald C. Spencer, is a map associated to a deformation of a scheme or complex manifold X, taking a tangent space of a point of the deformation space to the first cohomology group of the sheaf of vector fields on X. Glossary of algebraic geometry and Kodaira–Spencer map are algebraic geometry.

See Glossary of algebraic geometry and Kodaira–Spencer map

Kuranishi structure

In mathematics, especially in topology, a Kuranishi structure is a smooth analogue of scheme structure.

See Glossary of algebraic geometry and Kuranishi structure

Lelong number

In mathematics, the Lelong number is an invariant of a point of a complex analytic variety that in some sense measures the local density at that point.

See Glossary of algebraic geometry and Lelong number

Level structure (algebraic geometry)

In algebraic geometry, a level structure on a space X is an extra structure attached to X that shrinks or eliminates the automorphism group of X, by demanding automorphisms to preserve the level structure; attaching a level structure is often phrased as rigidifying the geometry of X. In applications, a level structure is used in the construction of moduli spaces; a moduli space is often constructed as a quotient. Glossary of algebraic geometry and level structure (algebraic geometry) are algebraic geometry.

See Glossary of algebraic geometry and Level structure (algebraic geometry)

Line at infinity

In geometry and topology, the line at infinity is a projective line that is added to the real (affine) plane in order to give closure to, and remove the exceptional cases from, the incidence properties of the resulting projective plane.

See Glossary of algebraic geometry and Line at infinity

Linear algebraic group

In mathematics, a linear algebraic group is a subgroup of the group of invertible n\times n matrices (under matrix multiplication) that is defined by polynomial equations.

See Glossary of algebraic geometry and Linear algebraic group

Linear system of divisors

In algebraic geometry, a linear system of divisors is an algebraic generalization of the geometric notion of a family of curves; the dimension of the linear system corresponds to the number of parameters of the family.

See Glossary of algebraic geometry and Linear system of divisors

List of complex and algebraic surfaces

This is a list of named algebraic surfaces, compact complex surfaces, and families thereof, sorted according to their Kodaira dimension following Enriques–Kodaira classification.

See Glossary of algebraic geometry and List of complex and algebraic surfaces

List of curves

This is a list of Wikipedia articles about curves used in different fields: mathematics (including geometry, statistics, and applied mathematics), physics, engineering, economics, medicine, biology, psychology, ecology, etc.

See Glossary of algebraic geometry and List of curves

List of surfaces

This is a list of surfaces in mathematics.

See Glossary of algebraic geometry and List of surfaces

Local cohomology

In algebraic geometry, local cohomology is an algebraic analogue of relative cohomology.

See Glossary of algebraic geometry and Local cohomology

Local uniformization

In algebraic geometry, local uniformization is a weak form of resolution of singularities, stating that a variety can be desingularized near any valuation, or in other words that the Zariski–Riemann space of the array is in some sense non-singular. Glossary of algebraic geometry and local uniformization are algebraic geometry.

See Glossary of algebraic geometry and Local uniformization

Localization (commutative algebra)

In commutative algebra and algebraic geometry, localization is a formal way to introduce the "denominators" to a given ring or module.

See Glossary of algebraic geometry and Localization (commutative algebra)

Log structure

In algebraic geometry, a log structure provides an abstract context to study semistable schemes, and in particular the notion of logarithmic differential form and the related Hodge-theoretic concepts. Glossary of algebraic geometry and log structure are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Log structure

Logarithmic form

In algebraic geometry and the theory of complex manifolds, a logarithmic differential form is a differential form with poles of a certain kind. Glossary of algebraic geometry and logarithmic form are algebraic geometry.

See Glossary of algebraic geometry and Logarithmic form

Loop group

In mathematics, a loop group (not to be confused with a loop) is a group of loops in a topological group G with multiplication defined pointwise.

See Glossary of algebraic geometry and Loop group

Minimal model program

In algebraic geometry, the minimal model program is part of the birational classification of algebraic varieties. Glossary of algebraic geometry and minimal model program are algebraic geometry.

See Glossary of algebraic geometry and Minimal model program

Moduli of algebraic curves

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism classes of algebraic curves.

See Glossary of algebraic geometry and Moduli of algebraic curves

Moduli space

In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind, or isomorphism classes of such objects.

See Glossary of algebraic geometry and Moduli space

Morphism of algebraic varieties

In algebraic geometry, a morphism between algebraic varieties is a function between the varieties that is given locally by polynomials.

See Glossary of algebraic geometry and Morphism of algebraic varieties

Morphism of schemes

In algebraic geometry, a morphism of schemes generalizes a morphism of algebraic varieties just as a scheme generalizes an algebraic variety. Glossary of algebraic geometry and morphism of schemes are algebraic geometry.

See Glossary of algebraic geometry and Morphism of schemes

Multiplicative group

In mathematics and group theory, the term multiplicative group refers to one of the following concepts.

See Glossary of algebraic geometry and Multiplicative group

Nagata's compactification theorem

In algebraic geometry, Nagata's compactification theorem, introduced by, implies that every abstract variety can be embedded in a complete variety, and more generally shows that a separated and finite type morphism to a Noetherian scheme S can be factored into an open immersion followed by a proper morphism.

See Glossary of algebraic geometry and Nagata's compactification theorem

Nef line bundle

In algebraic geometry, a line bundle on a projective variety is nef if it has nonnegative degree on every curve in the variety.

See Glossary of algebraic geometry and Nef line bundle

Nilpotent

In mathematics, an element x of a ring R is called nilpotent if there exists some positive integer n, called the index (or sometimes the degree), such that x^n.

See Glossary of algebraic geometry and Nilpotent

Noetherian ring

In mathematics, a Noetherian ring is a ring that satisfies the ascending chain condition on left and right ideals; if the chain condition is satisfied only for left ideals or for right ideals, then the ring is said left-Noetherian or right-Noetherian respectively.

See Glossary of algebraic geometry and Noetherian ring

Noetherian scheme

In algebraic geometry, a Noetherian scheme is a scheme that admits a finite covering by open affine subsets \operatornameSpec A_i, where each A_i is a Noetherian ring. Glossary of algebraic geometry and Noetherian scheme are algebraic geometry.

See Glossary of algebraic geometry and Noetherian scheme

Noetherian topological space

In mathematics, a Noetherian topological space, named for Emmy Noether, is a topological space in which closed subsets satisfy the descending chain condition. Glossary of algebraic geometry and Noetherian topological space are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Noetherian topological space

Noncommutative algebraic geometry

Noncommutative algebraic geometry is a branch of mathematics, and more specifically a direction in noncommutative geometry, that studies the geometric properties of formal duals of non-commutative algebraic objects such as rings as well as geometric objects derived from them (e.g. by gluing along localizations or taking noncommutative stack quotients). Glossary of algebraic geometry and noncommutative algebraic geometry are algebraic geometry.

See Glossary of algebraic geometry and Noncommutative algebraic geometry

Normal bundle

In differential geometry, a field of mathematics, a normal bundle is a particular kind of vector bundle, complementary to the tangent bundle, and coming from an embedding (or immersion). Glossary of algebraic geometry and normal bundle are algebraic geometry.

See Glossary of algebraic geometry and Normal bundle

Normal cone

In algebraic geometry, the normal cone of a subscheme of a scheme is a scheme analogous to the normal bundle or tubular neighborhood in differential geometry. Glossary of algebraic geometry and normal cone are algebraic geometry.

See Glossary of algebraic geometry and Normal cone

Normal crossing singularity

In algebraic geometry a normal crossing singularity is a singularity similar to a union of coordinate hyperplanes. Glossary of algebraic geometry and normal crossing singularity are algebraic geometry.

See Glossary of algebraic geometry and Normal crossing singularity

Normal scheme

In algebraic geometry, an algebraic variety or scheme X is normal if it is normal at every point, meaning that the local ring at the point is an integrally closed domain. Glossary of algebraic geometry and normal scheme are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Normal scheme

Open and closed maps

In mathematics, more specifically in topology, an open map is a function between two topological spaces that maps open sets to open sets.

See Glossary of algebraic geometry and Open and closed maps

Orbifold

In the mathematical disciplines of topology and geometry, an orbifold (for "orbit-manifold") is a generalization of a manifold.

See Glossary of algebraic geometry and Orbifold

Oscar Zariski

Oscar Zariski (April 24, 1899 – July 4, 1986) was an American mathematician.

See Glossary of algebraic geometry and Oscar Zariski

Picard group

In mathematics, the Picard group of a ringed space X, denoted by Pic(X), is the group of isomorphism classes of invertible sheaves (or line bundles) on X, with the group operation being tensor product. Glossary of algebraic geometry and Picard group are scheme theory.

See Glossary of algebraic geometry and Picard group

Plücker embedding

In mathematics, the Plücker map embeds the Grassmannian \mathbf(k,V), whose elements are k-dimensional subspaces of an n-dimensional vector space V, either real or complex, in a projective space, thereby realizing it as a projective algebraic variety. Glossary of algebraic geometry and Plücker embedding are algebraic geometry.

See Glossary of algebraic geometry and Plücker embedding

Poincaré residue

In mathematics, the Poincaré residue is a generalization, to several complex variables and complex manifold theory, of the residue at a pole of complex function theory.

See Glossary of algebraic geometry and Poincaré residue

Porteous formula

In mathematics, the Porteous formula, or Thom–Porteous formula, or Giambelli–Thom–Porteous formula, is an expression for the fundamental class of a degeneracy locus (or determinantal variety) of a morphism of vector bundles in terms of Chern classes.

See Glossary of algebraic geometry and Porteous formula

Prime ideal

In algebra, a prime ideal is a subset of a ring that shares many important properties of a prime number in the ring of integers.

See Glossary of algebraic geometry and Prime ideal

Proj construction

In algebraic geometry, Proj is a construction analogous to the spectrum-of-a-ring construction of affine schemes, which produces objects with the typical properties of projective spaces and projective varieties. Glossary of algebraic geometry and proj construction are scheme theory.

See Glossary of algebraic geometry and Proj construction

Projection formula

In algebraic geometry, the projection formula states the following: For a morphism f:X\to Y of ringed spaces, an \mathcal_X-module \mathcal and a locally free \mathcal_Y-module \mathcal of finite rank, the natural maps of sheaves are isomorphisms.

See Glossary of algebraic geometry and Projection formula

Projective bundle

In mathematics, a projective bundle is a fiber bundle whose fibers are projective spaces. Glossary of algebraic geometry and projective bundle are algebraic geometry.

See Glossary of algebraic geometry and Projective bundle

Projective geometry

In mathematics, projective geometry is the study of geometric properties that are invariant with respect to projective transformations.

See Glossary of algebraic geometry and Projective geometry

Projective space

In mathematics, the concept of a projective space originated from the visual effect of perspective, where parallel lines seem to meet at infinity.

See Glossary of algebraic geometry and Projective space

Projective variety

In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective ''n''-space \mathbb^n over k that is the zero-locus of some finite family of homogeneous polynomials of n + 1 variables with coefficients in k, that generate a prime ideal, the defining ideal of the variety. Glossary of algebraic geometry and projective variety are algebraic geometry.

See Glossary of algebraic geometry and Projective variety

Projectivization

In mathematics, projectivization is a procedure which associates with a non-zero vector space a projective space, whose elements are one-dimensional subspaces of.

See Glossary of algebraic geometry and Projectivization

Proper morphism

In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces.

See Glossary of algebraic geometry and Proper morphism

Pseudo-reductive group

In mathematics, a pseudo-reductive group over a field k (sometimes called a k-reductive group) is a smooth connected affine algebraic group defined over k whose k-unipotent radical (i.e., largest smooth connected unipotent normal k-subgroup) is trivial.

See Glossary of algebraic geometry and Pseudo-reductive group

Pullback (category theory)

In category theory, a branch of mathematics, a pullback (also called a fiber product, fibre product, fibered product or Cartesian square) is the limit of a diagram consisting of two morphisms and with a common codomain.

See Glossary of algebraic geometry and Pullback (category theory)

Quasi-compact morphism

In algebraic geometry, a morphism f: X \to Y between schemes is said to be quasi-compact if Y can be covered by open affine subschemes V_i such that the pre-images f^(V_i) are compact.

See Glossary of algebraic geometry and Quasi-compact morphism

Quasi-finite morphism

In algebraic geometry, a branch of mathematics, a morphism f: X → Y of schemes is quasi-finite if it is of finite type and satisfies any of the following equivalent conditions.

See Glossary of algebraic geometry and Quasi-finite morphism

Quasi-projective variety

In mathematics, a quasi-projective variety in algebraic geometry is a locally closed subset of a projective variety, i.e., the intersection inside some projective space of a Zariski-open and a Zariski-closed subset.

See Glossary of algebraic geometry and Quasi-projective variety

Quasi-separated morphism

In algebraic geometry, a morphism of schemes from to is called quasi-separated if the diagonal map from to is quasi-compact (meaning that the inverse image of any quasi-compact open set is quasi-compact). Glossary of algebraic geometry and quasi-separated morphism are algebraic geometry.

See Glossary of algebraic geometry and Quasi-separated morphism

Quasi-split group

In mathematics, a quasi-split group over a field is a reductive group with a Borel subgroup defined over the field.

See Glossary of algebraic geometry and Quasi-split group

Quot scheme

In algebraic geometry, the Quot scheme is a scheme parametrizing sheaves on a projective scheme. Glossary of algebraic geometry and Quot scheme are algebraic geometry.

See Glossary of algebraic geometry and Quot scheme

Quotient stack

In algebraic geometry, a quotient stack is a stack that parametrizes equivariant objects. Glossary of algebraic geometry and quotient stack are algebraic geometry.

See Glossary of algebraic geometry and Quotient stack

Radicial morphism

In algebraic geometry, a morphism of schemes is called radicial or universally injective, if, for every field K the induced map X(K) → Y(K) is injective.

See Glossary of algebraic geometry and Radicial morphism

Ramification (mathematics)

In geometry, ramification is 'branching out', in the way that the square root function, for complex numbers, can be seen to have two branches differing in sign.

See Glossary of algebraic geometry and Ramification (mathematics)

Rational normal curve

In mathematics, the rational normal curve is a smooth, rational curve of degree in projective n-space.

See Glossary of algebraic geometry and Rational normal curve

Rational normal scroll

In mathematics, a rational normal scroll is a ruled surface of degree n in projective space of dimension n + 1. Glossary of algebraic geometry and rational normal scroll are algebraic geometry.

See Glossary of algebraic geometry and Rational normal scroll

Rational point

In number theory and algebraic geometry, a rational point of an algebraic variety is a point whose coordinates belong to a given field.

See Glossary of algebraic geometry and Rational point

Rational singularity

In mathematics, more particularly in the field of algebraic geometry, a scheme X has rational singularities, if it is normal, of finite type over a field of characteristic zero, and there exists a proper birational map from a regular scheme Y such that the higher direct images of f_* applied to \mathcal_Y are trivial.

See Glossary of algebraic geometry and Rational singularity

Rational surface

In algebraic geometry, a branch of mathematics, a rational surface is a surface birationally equivalent to the projective plane, or in other words a rational variety of dimension two.

See Glossary of algebraic geometry and Rational surface

Rational variety

In mathematics, a rational variety is an algebraic variety, over a given field K, which is birationally equivalent to a projective space of some dimension over K. This means that its function field is isomorphic to the field of all rational functions for some set \ of indeterminates, where d is the dimension of the variety.

See Glossary of algebraic geometry and Rational variety

Real form (Lie theory)

In mathematics, the notion of a real form relates objects defined over the field of real and complex numbers.

See Glossary of algebraic geometry and Real form (Lie theory)

Reduced ring

In ring theory, a branch of mathematics, a ring is called a reduced ring if it has no non-zero nilpotent elements.

See Glossary of algebraic geometry and Reduced ring

Reductive group

In mathematics, a reductive group is a type of linear algebraic group over a field.

See Glossary of algebraic geometry and Reductive group

Reflexive sheaf

In algebraic geometry, a reflexive sheaf is a coherent sheaf that is isomorphic to its second dual (as a sheaf of modules) via the canonical map.

See Glossary of algebraic geometry and Reflexive sheaf

Regular embedding

In algebraic geometry, a closed immersion i: X \hookrightarrow Y of schemes is a regular embedding of codimension r if each point x in X has an open affine neighborhood U in Y such that the ideal of X \cap U is generated by a regular sequence of length r. A regular embedding of codimension one is precisely an effective Cartier divisor.

See Glossary of algebraic geometry and Regular embedding

Regular local ring

In commutative algebra, a regular local ring is a Noetherian local ring having the property that the minimal number of generators of its maximal ideal is equal to its Krull dimension. Glossary of algebraic geometry and regular local ring are algebraic geometry.

See Glossary of algebraic geometry and Regular local ring

Regular scheme

In algebraic geometry, a regular scheme is a locally Noetherian scheme whose local rings are regular everywhere. Glossary of algebraic geometry and regular scheme are algebraic geometry and scheme theory.

See Glossary of algebraic geometry and Regular scheme

Regular sequence

In commutative algebra, a regular sequence is a sequence of elements of a commutative ring which are as independent as possible, in a precise sense.

See Glossary of algebraic geometry and Regular sequence

Representable functor

In mathematics, particularly category theory, a representable functor is a certain functor from an arbitrary category into the category of sets.

See Glossary of algebraic geometry and Representable functor

Research program

A research program (British English: research programme) is a professional network of scientists conducting basic research.

See Glossary of algebraic geometry and Research program

Residue field

In mathematics, the residue field is a basic construction in commutative algebra. Glossary of algebraic geometry and residue field are algebraic geometry.

See Glossary of algebraic geometry and Residue field

Resolution of singularities

In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, which is a non-singular variety W with a proper birational map W→V. Glossary of algebraic geometry and resolution of singularities are algebraic geometry.

See Glossary of algebraic geometry and Resolution of singularities

Riemann hypothesis

In mathematics, the Riemann hypothesis is the conjecture that the Riemann zeta function has its zeros only at the negative even integers and complex numbers with real part.

See Glossary of algebraic geometry and Riemann hypothesis

Riemann–Hurwitz formula

In mathematics, the Riemann–Hurwitz formula, named after Bernhard Riemann and Adolf Hurwitz, describes the relationship of the Euler characteristics of two surfaces when one is a ramified covering of the other.

See Glossary of algebraic geometry and Riemann–Hurwitz formula

Riemann–Roch theorem

The Riemann–Roch theorem is an important theorem in mathematics, specifically in complex analysis and algebraic geometry, for the computation of the dimension of the space of meromorphic functions with prescribed zeros and allowed poles.

See Glossary of algebraic geometry and Riemann–Roch theorem

Ring of polynomial functions

In mathematics, the ring of polynomial functions on a vector space V over a field k gives a coordinate-free analog of a polynomial ring.

See Glossary of algebraic geometry and Ring of polynomial functions

Ring spectrum

In stable homotopy theory, a ring spectrum is a spectrum E together with a multiplication map and a unit map where S is the sphere spectrum.

See Glossary of algebraic geometry and Ring spectrum

Ringed space

In mathematics, a ringed space is a family of (commutative) rings parametrized by open subsets of a topological space together with ring homomorphisms that play roles of restrictions. Glossary of algebraic geometry and ringed space are scheme theory.

See Glossary of algebraic geometry and Ringed space

Séminaire de Géométrie Algébrique du Bois Marie

In mathematics, the Séminaire de Géométrie Algébrique du Bois Marie (SGA) was an influential seminar run by Alexander Grothendieck. Glossary of algebraic geometry and Séminaire de Géométrie Algébrique du Bois Marie are scheme theory.

See Glossary of algebraic geometry and Séminaire de Géométrie Algébrique du Bois Marie

Scheme (mathematics)

In mathematics, specifically algebraic geometry, a scheme is a structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x. Glossary of algebraic geometry and scheme (mathematics) are scheme theory.

See Glossary of algebraic geometry and Scheme (mathematics)

Schubert variety

In algebraic geometry, a Schubert variety is a certain subvariety of a Grassmannian, \mathbf_k(V) of k-dimensional subspaces of a vector space V, usually with singular points. Glossary of algebraic geometry and Schubert variety are algebraic geometry.

See Glossary of algebraic geometry and Schubert variety

Secant variety

In algebraic geometry, the secant variety \operatorname(V), or the variety of chords, of a projective variety V \subset \mathbb^r is the Zariski closure of the union of all secant lines (chords) to V in \mathbb^r: (for x. Glossary of algebraic geometry and secant variety are algebraic geometry.

See Glossary of algebraic geometry and Secant variety

Separable extension

In field theory, a branch of algebra, an algebraic field extension E/F is called a separable extension if for every \alpha\in E, the minimal polynomial of \alpha over is a separable polynomial (i.e., its formal derivative is not the zero polynomial, or equivalently it has no repeated roots in any extension field).

See Glossary of algebraic geometry and Separable extension

Serre duality

In algebraic geometry, a branch of mathematics, Serre duality is a duality for the coherent sheaf cohomology of algebraic varieties, proved by Jean-Pierre Serre.

See Glossary of algebraic geometry and Serre duality

Serre's criterion for normality

In algebra, Serre's criterion for normality, introduced by Jean-Pierre Serre, gives necessary and sufficient conditions for a commutative Noetherian ring A to be a normal ring.

See Glossary of algebraic geometry and Serre's criterion for normality

Sheaf (mathematics)

In mathematics, a sheaf (sheaves) is a tool for systematically tracking data (such as sets, abelian groups, rings) attached to the open sets of a topological space and defined locally with regard to them.

See Glossary of algebraic geometry and Sheaf (mathematics)

Sheaf of algebras

In algebraic geometry, a sheaf of algebras on a ringed space X is a sheaf of commutative rings on X that is also a sheaf of \mathcalO_X-modules.

See Glossary of algebraic geometry and Sheaf of algebras

Sheaf of modules

In mathematics, a sheaf of O-modules or simply an O-module over a ringed space (X, O) is a sheaf F such that, for any open subset U of X, F(U) is an O(U)-module and the restriction maps F(U) → F(V) are compatible with the restriction maps O(U) → O(V): the restriction of fs is the restriction of f times the restriction of s for any f in O(U) and s in F(U).

See Glossary of algebraic geometry and Sheaf of modules

Singular point of an algebraic variety

In the mathematical field of algebraic geometry, a singular point of an algebraic variety is a point that is 'special' (so, singular), in the geometric sense that at this point the tangent space at the variety may not be regularly defined.

See Glossary of algebraic geometry and Singular point of an algebraic variety

Smooth scheme

In algebraic geometry, a smooth scheme over a field is a scheme which is well approximated by affine space near any point. Glossary of algebraic geometry and smooth scheme are scheme theory.

See Glossary of algebraic geometry and Smooth scheme

Solvable group

In mathematics, more specifically in the field of group theory, a solvable group or soluble group is a group that can be constructed from abelian groups using extensions.

See Glossary of algebraic geometry and Solvable group

Spectrum of a ring

In commutative algebra, the prime spectrum (or simply the spectrum) of a commutative ring R is the set of all prime ideals of R, and is usually denoted by \operatorname; in algebraic geometry it is simultaneously a topological space equipped with the sheaf of rings \mathcal. Glossary of algebraic geometry and spectrum of a ring are scheme theory.

See Glossary of algebraic geometry and Spectrum of a ring

Spherical variety

In algebraic geometry, given a reductive algebraic group G and a Borel subgroup B, a spherical variety is a G-variety with an open dense B-orbit. Glossary of algebraic geometry and spherical variety are algebraic geometry.

See Glossary of algebraic geometry and Spherical variety

Split Lie algebra

In the mathematical field of Lie theory, a split Lie algebra is a pair (\mathfrak, \mathfrak) where \mathfrak is a Lie algebra and \mathfrak is a splitting Cartan subalgebra, where "splitting" means that for all x \in \mathfrak, \operatorname_ x is triangularizable.

See Glossary of algebraic geometry and Split Lie algebra

Springer Science+Business Media

Springer Science+Business Media, commonly known as Springer, is a German multinational publishing company of books, e-books and peer-reviewed journals in science, humanities, technical and medical (STM) publishing.

See Glossary of algebraic geometry and Springer Science+Business Media

Stable curve

In algebraic geometry, a stable curve is an algebraic curve that is asymptotically stable in the sense of geometric invariant theory.

See Glossary of algebraic geometry and Stable curve

Stable vector bundle

In mathematics, a stable vector bundle is a (holomorphic or algebraic) vector bundle that is stable in the sense of geometric invariant theory. Glossary of algebraic geometry and stable vector bundle are algebraic geometry.

See Glossary of algebraic geometry and Stable vector bundle

Stack (mathematics)

In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes values in categories rather than sets. Glossary of algebraic geometry and stack (mathematics) are algebraic geometry.

See Glossary of algebraic geometry and Stack (mathematics)

Stein factorization

In algebraic geometry, the Stein factorization, introduced by for the case of complex spaces, states that a proper morphism can be factorized as a composition of a finite mapping and a proper morphism with connected fibers. Glossary of algebraic geometry and Stein factorization are algebraic geometry.

See Glossary of algebraic geometry and Stein factorization

Symmetric space

In mathematics, a symmetric space is a Riemannian manifold (or more generally, a pseudo-Riemannian manifold) whose group of isometries contains an inversion symmetry about every point.

See Glossary of algebraic geometry and Symmetric space

Symmetric variety

In algebraic geometry, a symmetric variety is an algebraic analogue of a symmetric space in differential geometry, given by a quotient G/H of a reductive algebraic group G by the subgroup ''H'' fixed by some involution of G. Glossary of algebraic geometry and symmetric variety are algebraic geometry.

See Glossary of algebraic geometry and Symmetric variety

Tautological bundle

In mathematics, the tautological bundle is a vector bundle occurring over a Grassmannian in a natural tautological way: for a Grassmannian of k-dimensional subspaces of V, given a point in the Grassmannian corresponding to a k-dimensional vector subspace W \subseteq V, the fiber over W is the subspace W itself.

See Glossary of algebraic geometry and Tautological bundle

Tensor product

In mathematics, the tensor product V \otimes W of two vector spaces and (over the same field) is a vector space to which is associated a bilinear map V\times W \rightarrow V\otimes W that maps a pair (v,w),\ v\in V, w\in W to an element of V \otimes W denoted.

See Glossary of algebraic geometry and Tensor product

Tensor product of algebras

In mathematics, the tensor product of two algebras over a commutative ring R is also an R-algebra.

See Glossary of algebraic geometry and Tensor product of algebras

Theorem on formal functions

In algebraic geometry, the theorem on formal functions states the following: The theorem is used to deduce some other important theorems: Stein factorization and a version of Zariski's main theorem that says that a proper birational morphism into a normal variety is an isomorphism.

See Glossary of algebraic geometry and Theorem on formal functions

Todd class

In mathematics, the Todd class is a certain construction now considered a part of the theory in algebraic topology of characteristic classes.

See Glossary of algebraic geometry and Todd class

Topological space

In mathematics, a topological space is, roughly speaking, a geometrical space in which closeness is defined but cannot necessarily be measured by a numeric distance.

See Glossary of algebraic geometry and Topological space

Toric variety

In algebraic geometry, a toric variety or torus embedding is an algebraic variety containing an algebraic torus as an open dense subset, such that the action of the torus on itself extends to the whole variety. Glossary of algebraic geometry and toric variety are algebraic geometry.

See Glossary of algebraic geometry and Toric variety

Torsor (algebraic geometry)

In algebraic geometry, a torsor or a principal bundle is an analogue of a principal bundle in algebraic topology. Glossary of algebraic geometry and torsor (algebraic geometry) are algebraic geometry.

See Glossary of algebraic geometry and Torsor (algebraic geometry)

Tropical geometry

In mathematics, tropical geometry is the study of polynomials and their geometric properties when addition is replaced with minimization and multiplication is replaced with ordinary addition: So for example, the classical polynomial x^3 + 2xy + y^4 would become \min\. Glossary of algebraic geometry and tropical geometry are algebraic geometry.

See Glossary of algebraic geometry and Tropical geometry

Twisted cubic

In mathematics, a twisted cubic is a smooth, rational curve C of degree three in projective 3-space P3.

See Glossary of algebraic geometry and Twisted cubic

Unique factorization domain

In mathematics, a unique factorization domain (UFD) (also sometimes called a factorial ring following the terminology of Bourbaki) is a ring in which a statement analogous to the fundamental theorem of arithmetic holds.

See Glossary of algebraic geometry and Unique factorization domain

Universal property

In mathematics, more specifically in category theory, a universal property is a property that characterizes up to an isomorphism the result of some constructions.

See Glossary of algebraic geometry and Universal property

Unramified morphism

In algebraic geometry, an unramified morphism is a morphism f: X \to Y of schemes such that (a) it is locally of finite presentation and (b) for each x \in X and y. Glossary of algebraic geometry and unramified morphism are algebraic geometry.

See Glossary of algebraic geometry and Unramified morphism

Valuation ring

In abstract algebra, a valuation ring is an integral domain D such that for every non-zero element x of its field of fractions F, at least one of x or x−1 belongs to D. Given a field F, if D is a subring of F such that either x or x−1 belongs to D for every nonzero x in F, then D is said to be a valuation ring for the field F or a place of F.

See Glossary of algebraic geometry and Valuation ring

Vector bundle

In mathematics, a vector bundle is a topological construction that makes precise the idea of a family of vector spaces parameterized by another space X (for example X could be a topological space, a manifold, or an algebraic variety): to every point x of the space X we associate (or "attach") a vector space V(x) in such a way that these vector spaces fit together to form another space of the same kind as X (e.g.

See Glossary of algebraic geometry and Vector bundle

Virtual fundamental class

In mathematics, specifically enumerative geometry, the virtual fundamental class ^\text_ of a space X is a replacement of the classical fundamental class \in A^*(X) in its Chow ring which has better behavior with respect to the enumerative problems being considered.

See Glossary of algebraic geometry and Virtual fundamental class

Weil reciprocity law

In mathematics, the Weil reciprocity law is a result of André Weil holding in the function field K(C) of an algebraic curve C over an algebraically closed field K. Given functions f and g in K(C), i.e. rational functions on C, then where the notation has this meaning: (h) is the divisor of the function h, or in other words the formal sum of its zeroes and poles counted with multiplicity; and a function applied to a formal sum means the product (with multiplicities, poles counting as a negative multiplicity) of the values of the function at the points of the divisor.

See Glossary of algebraic geometry and Weil reciprocity law

Yoneda lemma

In mathematics, the Yoneda lemma is a fundamental result in category theory.

See Glossary of algebraic geometry and Yoneda lemma

Zariski tangent space

In algebraic geometry, the Zariski tangent space is a construction that defines a tangent space at a point P on an algebraic variety V (and more generally). Glossary of algebraic geometry and Zariski tangent space are algebraic geometry.

See Glossary of algebraic geometry and Zariski tangent space

Zariski topology

In algebraic geometry and commutative algebra, the Zariski topology is a topology defined on geometric objects called varieties. Glossary of algebraic geometry and Zariski topology are scheme theory.

See Glossary of algebraic geometry and Zariski topology

Zariski's main theorem

In algebraic geometry, Zariski's main theorem, proved by, is a statement about the structure of birational morphisms stating roughly that there is only one branch at any normal point of a variety.

See Glossary of algebraic geometry and Zariski's main theorem

Zariski–Riemann space

In algebraic geometry, a Zariski–Riemann space or Zariski space of a subring k of a field K is a locally ringed space whose points are valuation rings containing k and contained in K. They generalize the Riemann surface of a complex curve. Glossary of algebraic geometry and Zariski–Riemann space are algebraic geometry.

See Glossary of algebraic geometry and Zariski–Riemann space

See also

Glossaries of mathematics

• Glossary of Lie groups and Lie algebras
• Glossary of Principia Mathematica
• Glossary of Riemannian and metric geometry
• Glossary of algebraic geometry
• Glossary of algebraic topology
• Glossary of areas of mathematics
• Glossary of arithmetic and diophantine geometry
• Glossary of calculus
• Glossary of category theory
• Glossary of classical algebraic geometry
• Glossary of commutative algebra
• Glossary of cryptographic keys
• Glossary of differential geometry and topology
• Glossary of experimental design
• Glossary of field theory
• Glossary of functional analysis
• Glossary of game theory
• Glossary of general topology
• Glossary of graph theory
• Glossary of group theory
• Glossary of invariant theory
• Glossary of linear algebra
• Glossary of mathematical jargon
• Glossary of mathematical symbols
• Glossary of module theory
• Glossary of number theory
• Glossary of order theory
• Glossary of probability and statistics
• Glossary of real and complex analysis
• Glossary of representation theory
• Glossary of ring theory
• Glossary of set theory
• Glossary of shapes with metaphorical names
• Glossary of symplectic geometry
• Glossary of systems theory
• Glossary of tensor theory

Scheme theory

• Éléments de géométrie algébrique
• Étale fundamental group
• Étale group scheme
• Azumaya algebra
• Chevalley scheme
• Derived algebraic geometry
• Equivariant sheaf
• Essentially finite vector bundle
• Fiber product of schemes
• Formal scheme
• Function field (scheme theory)
• Fundamental group scheme
• Gabriel–Rosenberg reconstruction theorem
• Geometric invariant theory
• Geometrically (algebraic geometry)
• Glossary of algebraic geometry
• Gluing schemes
• Gorenstein scheme
• Grothendieck's relative point of view
• Group scheme
• Groupoid object
• Hilbert scheme
• Ideal sheaf
• Log structure
• Noetherian topological space
• Nori-semistable vector bundle
• Normal scheme
• Picard group
• Proj construction
• Quotient by an equivalence relation
• Regular scheme
• Ringed space
• Séminaire de Géométrie Algébrique du Bois Marie
• Scheme (mathematics)
• Severi variety (Hilbert scheme)
• Smooth scheme
• Spectrum of a ring
• Valuative criterion
• Weil restriction
• Zariski topology

References

[1] https://en.wikipedia.org/wiki/Glossary_of_algebraic_geometry

Also known as Affine cover, Algebraic scheme, Artinian scheme, Artinian subscheme, Closed subscheme, Conductor (algebraic geometry), Connected scheme, Finitely presented scheme, Geometric fiber, Geometric fibre, Geometric point, Geometric property, Glossary of scheme theory, Glossary of stack theory, Good quotient, Immersion (algebraic geometry), Integral scheme, Locally of finite presentation, Locally of finite type, Open immersion, Open subscheme, Projective morphism, Pure dimension, Reduced scheme, Representable morphism of stacks, Ring of sections, Scheme theoretic image, Scheme-theoretic image, Section ring, Subscheme.

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