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63 relations: Abelian variety, Albanese variety, Alexei Skorobogatov, Algebraic curve, André Néron, Arithmetic dynamics, Arzelà–Ascoli theorem, Beauville–Laszlo theorem, Birch and Swinnerton-Dyer conjecture, Borel fixed-point theorem, Brauer group, Chow group, Classification of discontinuities, Congruent number, Conjecture, Cubic plane curve, Diophantine equation, Diophantine geometry, Divisor (algebraic geometry), EdDSA, Elliptic curve, Euler's sum of powers conjecture, Faltings's theorem, Fiber product of schemes, Field arithmetic, Genus (mathematics), Glossary of algebraic geometry, Glossary of areas of mathematics, Glossary of field theory, Goppa code, Graph coloring, Group of Lie type, Group of rational points on the unit circle, Heath-Brown–Moroz constant, Heegner point, Inverse curve, Kneser–Tits conjecture, Kobayashi metric, Linear algebraic group, List of mathematical properties of points, Mordell–Weil theorem, Nagell–Lutz theorem, Néron–Tate height, Number theory, Pierre de Fermat, Principal homogeneous space, Projective variety, Proof by infinite descent, Pseudo algebraically closed field, Pythagorean triple, ..., Rational (disambiguation), Rational number, Reductive group, Residue field, Riemann integral, Scheme (mathematics), Stereographic projection, Tangent space to a functor, Tate–Shafarevich group, Theorem of Bertini, Weil conjectures, Wieferich prime, Zariski tangent space. Expand index (13 more) »
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.
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Albanese variety
In mathematics, the Albanese variety A(V), named for Giacomo Albanese, is a generalization of the Jacobian variety of a curve.
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Alexei Skorobogatov
Alexei Nikolaievich Skorobogatov (Алексе́й Никола́евич Скоробога́тов) - a British-Russian mathematician, a Professor in Pure Mathematics at Imperial College London specialising in algebraic geometry.
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Algebraic curve
In mathematics, a plane real algebraic curve is the set of points on the Euclidean plane whose coordinates are zeros of some polynomial in two variables.
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André Néron
André Néron (November 30, 1922, La Clayette, France – April 6, 1985, Paris, France) was a French mathematician at the Université de Poitiers who worked on elliptic curves and Abelian varieties.
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Arithmetic dynamics
Arithmetic dynamics is a field that amalgamates two areas of mathematics, dynamical systems and number theory.
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Arzelà–Ascoli theorem
The Arzelà–Ascoli theorem is a fundamental result of mathematical analysis giving necessary and sufficient conditions to decide whether every sequence of a given family of real-valued continuous functions defined on a closed and bounded interval has a uniformly convergent subsequence.
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Beauville–Laszlo theorem
In mathematics, the Beauville–Laszlo theorem is a result in commutative algebra and algebraic geometry that allows one to "glue" two sheaves over an infinitesimal neighborhood of a point on an algebraic curve.
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Birch and Swinnerton-Dyer conjecture
In mathematics, the Birch and Swinnerton-Dyer conjecture describes the set of rational solutions to equations defining an elliptic curve.
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Borel fixed-point theorem
In mathematics, the Borel fixed-point theorem is a fixed-point theorem in algebraic geometry generalizing the Lie–Kolchin theorem.
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Brauer group
In mathematics, the Brauer group of a field K is an abelian group whose elements are Morita equivalence classes of central simple algebras over K, with addition given by the tensor product of algebras.
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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.
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Classification of discontinuities
Continuous functions are of utmost importance in mathematics, functions and applications.
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Congruent number
In mathematics, a congruent number is a positive integer that is the area of a right triangle with three rational number sides.
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Conjecture
In mathematics, a conjecture is a conclusion or proposition based on incomplete information, for which no proof has been found.
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Cubic plane curve
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation applied to homogeneous coordinates for the projective plane; or the inhomogeneous version for the affine space determined by setting in such an equation.
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Diophantine equation
In mathematics, a Diophantine equation is a polynomial equation, usually in two or more unknowns, such that only the integer solutions are sought or studied (an integer solution is a solution such that all the unknowns take integer values).
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Diophantine geometry
In mathematics, diophantine geometry is one approach to the theory of Diophantine equations, formulating questions about such equations in terms of algebraic geometry over a ground field K that is not algebraically closed, such as the field of rational numbers or a finite field, or more general commutative ring such as the integers.
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Divisor (algebraic geometry)
In algebraic geometry, divisors are a generalization of codimension-1 subvarieties of algebraic varieties.
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EdDSA
In public-key cryptography, Edwards-curve Digital Signature Algorithm (EdDSA) is a digital signature scheme using a variant of Schnorr signature based on Twisted Edwards curves.
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Elliptic curve
In mathematics, an elliptic curve is a plane algebraic curve defined by an equation of the form which is non-singular; that is, the curve has no cusps or self-intersections.
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Euler's sum of powers conjecture
Euler's conjecture is a disproved conjecture in mathematics related to Fermat's last theorem.
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Faltings's theorem
In number theory, the Mordell conjecture is the conjecture made by that a curve of genus greater than 1 over the field Q of rational numbers has only finitely many rational points.
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Fiber product of schemes
In mathematics, specifically in algebraic geometry, the fiber product of schemes is a fundamental construction.
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Field arithmetic
In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a and its absolute Galois group.
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Genus (mathematics)
In mathematics, genus (plural genera) has a few different, but closely related, meanings.
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Glossary of algebraic geometry
This is a glossary of algebraic geometry.
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Glossary of areas of mathematics
This is a glossary of terms that are or have been considered areas of study in mathematics.
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Glossary of field theory
Field theory is the branch of mathematics in which fields are studied.
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Goppa code
In mathematics, an algebraic geometric code (AG-code), otherwise known as a Goppa code, is a general type of linear code constructed by using an algebraic curve X over a finite field \mathbb_q.
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Graph coloring
In graph theory, graph coloring is a special case of graph labeling; it is an assignment of labels traditionally called "colors" to elements of a graph subject to certain constraints.
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Group of Lie type
In mathematics, specifically in group theory, the phrase group of Lie type usually refers to finite groups that are closely related to the group of rational points of a reductive linear algebraic group with values in a finite field.
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Group of rational points on the unit circle
In mathematics, the rational points on the unit circle are those points (x, y) such that both x and y are rational numbers ("fractions") and satisfy x2 + y2.
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Heath-Brown–Moroz constant
The Heath-Brown–Moroz constant C, named for Roger Heath-Brown and Boris Moroz, is defined as where p runs over the primes.
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Heegner point
In mathematics, a Heegner point is a point on a modular curve that is the image of a quadratic imaginary point of the upper half-plane.
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Inverse curve
In inversive geometry, an inverse curve of a given curve is the result of applying an inverse operation to.
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Kneser–Tits conjecture
In mathematics, the Kneser–Tits problem, introduced by based on a suggestion by Martin Kneser, asks whether the Whitehead group W(G,K) of a semisimple simply connected isotropic algebraic group G over a field K is trivial.
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Kobayashi metric
In mathematics and especially complex geometry, the Kobayashi metric is a pseudometric intrinsically associated to any complex manifold.
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Linear algebraic group
In mathematics, a linear algebraic group is a subgroup of the group of invertible n×n matrices (under matrix multiplication) that is defined by polynomial equations.
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List of mathematical properties of points
In mathematics, the following appear.
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Mordell–Weil theorem
In mathematics, the Mordell–Weil theorem states that for an abelian variety A over a number field K, the group A(K) of ''K''-rational points of A is a finitely-generated abelian group, called the Mordell-Weil group.
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Nagell–Lutz theorem
In mathematics, the Nagell–Lutz theorem is a result in the diophantine geometry of elliptic curves, which describes rational torsion points on elliptic curves over the integers.
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Néron–Tate height
In number theory, the Néron–Tate height (or canonical height) is a quadratic form on the Mordell-Weil group of rational points of an abelian variety defined over a global field.
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Number theory
Number theory, or in older usage arithmetic, is a branch of pure mathematics devoted primarily to the study of the integers.
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Pierre de Fermat
Pierre de Fermat (Between 31 October and 6 December 1607 – 12 January 1665) was a French lawyer at the Parlement of Toulouse, France, and a mathematician who is given credit for early developments that led to infinitesimal calculus, including his technique of adequality.
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Principal homogeneous space
In mathematics, a principal homogeneous space, or torsor, for a group G is a homogeneous space X for G in which the stabilizer subgroup of every point is trivial.
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Projective variety
In algebraic geometry, a projective variety over an algebraically closed field k is a subset of some projective ''n''-space Pn 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.
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Proof by infinite descent
In mathematics, a proof by infinite descent is a particular kind of proof by contradiction that relies on the least integer principle.
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Pseudo algebraically closed field
In mathematics, a field K is pseudo algebraically closed if it satisfies certain properties which hold for any algebraically closed field.
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Pythagorean triple
A Pythagorean triple consists of three positive integers,, and, such that.
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Rational (disambiguation)
Rational may refer to.
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Rational number
In mathematics, a rational number is any number that can be expressed as the quotient or fraction of two integers, a numerator and a non-zero denominator.
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Reductive group
In mathematics, a reductive group is a type of linear algebraic group over a field.
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Residue field
In mathematics, the residue field is a basic construction in commutative algebra.
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Riemann integral
In the branch of mathematics known as real analysis, the Riemann integral, created by Bernhard Riemann, was the first rigorous definition of the integral of a function on an interval.
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Scheme (mathematics)
In mathematics, a scheme is a mathematical structure that enlarges the notion of algebraic variety in several ways, such as taking account of multiplicities (the equations x.
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Stereographic projection
In geometry, the stereographic projection is a particular mapping (function) that projects a sphere onto a plane.
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Tangent space to a functor
In algebraic geometry, the tangent space to a functor generalizes the classical construction of a tangent space such as the Zariski tangent space.
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Tate–Shafarevich group
In arithmetic geometry, the Tate–Shafarevich group Ш(A/K), introduced by and, of an abelian variety A (or more generally a group scheme) defined over a number field K consists of the elements of the Weil–Châtelet group WC(A/K).
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Theorem of Bertini
In mathematics, the theorem of Bertini is an existence and genericity theorem for smooth connected hyperplane sections for smooth projective varieties over algebraically closed fields, introduced by Eugenio Bertini.
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Weil conjectures
In mathematics, the Weil conjectures were some highly influential proposals by on the generating functions (known as local zeta-functions) derived from counting the number of points on algebraic varieties over finite fields.
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Wieferich prime
In number theory, a Wieferich prime is a prime number p such that p2 divides, therefore connecting these primes with Fermat's little theorem, which states that every odd prime p divides.
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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).
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Redirects here:
K-rational point, Rational points.
References
[1] https://en.wikipedia.org/wiki/Rational_point
