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274 relations: Abelian category, Absolute Galois group, Accessible category, Adjoint functors, Affine space, Alexander, Algebraic cycle, Algebraic differential equation, Algebraic geometry, Algebraic geometry and analytic geometry, Algebraic K-theory, Algebraic space, Algebraic topology, Algebraic torus, Algebraic variety, Ample line bundle, Anabelian geometry, Anarchism in France, André Joyal, André Weil, Angus Macintyre, Approximation property, Arithmetic zeta function, Ax–Grothendieck theorem, Azumaya algebra, ∞-topos, École normale supérieure (Paris), Éléments de géométrie algébrique, Émile Picard Medal, Étale cohomology, Étale fundamental group, Étale topology, Île de la Jatte, Banach space, Barry Mazur, Beck's monadicity theorem, Brauer group, Brieskorn–Grothendieck resolution, Bundle of principal parts, C. P. Ramanujam, Chern class, Chow group, Claude Chevalley, Coherent sheaf cohomology, Cohomology, Colin McLarty, Commutative algebra, Connection (mathematics), Constructible set (topology), Cotangent complex, ..., Crafoord Prize, Crystalline cohomology, Cyclic homology, D-module, Daniel Quillen, Dévissage, Deaths in November 2014, Deformation theory, Delta-functor, Derivator, Derived category, Descent (mathematics), Dessin d'enfant, Dieudonné module, Divisor (algebraic geometry), Dolbeault cohomology, Dunford–Pettis property, Dvoretzky's theorem, Element (category theory), Esquisse d'un Programme, Excellent ring, Exceptional inverse image functor, Fiber product of schemes, Field of definition, Fields Medal, Finite morphism, Fondements de la Géometrie Algébrique, Formally smooth map, Foundations of Algebraic Geometry, Fredholm kernel, French mathematical seminars, Fundamental group, Fundamental group scheme, G-ring, Galois extension, Galois module, Galois theory, Generic flatness, Geometric invariant theory, Geometry, George Mackey, Gerbe, Globular set, Glossary of areas of mathematics, Glossary of arithmetic and diophantine geometry, Glossary of category theory, Glossary of classical algebraic geometry, Glossary of commutative algebra, Grothendieck category, Grothendieck construction, Grothendieck group, Grothendieck inequality, Grothendieck space, Grothendieck topology, Grothendieck universe, Grothendieck's Galois theory, Grothendieck's relative point of view, Grothendieck's Tôhoku paper, Grothendieck–Katz p-curvature conjecture, Grothendieck–Riemann–Roch theorem, Grothendieck–Teichmüller group, Group scheme, Henri Cartan, Hilbert's problems, History of geometry, History of mathematical notation, History of mathematics, History of topos theory, Hoàng Xuân Sính, Hodge structure, Homological algebra, Homotopy hypothesis, Hyperfunction, Inaccessible cardinal, Injective sheaf, Institut des Hautes Études Scientifiques, Integrally closed domain, Internment camps in France, Inverse limit, Inverse system, Λ-ring, Jean Dieudonné, Jean Giraud (mathematician), Jean-Louis Verdier, Jean-Pierre Serre, John Edensor Littlewood, K-theory, Künneth theorem, Kunihiko Kodaira, Lasserre, Ariège, Laurent Schwartz, Léon Motchane, Le Chambon-sur-Lignon, Le Collège-Lycée Cévenol International, Lefschetz hyperplane theorem, Leila Schneps, Leray spectral sequence, List of algebraic geometry topics, List of École normale supérieure people, List of Brazilian scientists, List of countries by number of Fields Medallists, List of Fields Medal winners by university affiliation, List of French scientists, List of geometers, List of German inventors and discoverers, List of Holocaust survivors, List of important publications in mathematics, List of International Congresses of Mathematicians Plenary and Invited Speakers, List of Jewish mathematicians, List of mathematicians (G), List of Occitans, List of people by Erdős number, List of recluses, List of refugees, List of things named after Alexander Grothendieck, Local cohomology, Local zeta-function, Localizing subcategory, Lorenzo Ramero, Luc Illusie, March 1928, March 28, Masaki Kashiwara, Max Karoubi, Mende, Lozère, Michael Atiyah, Michel Demazure, Michel Raynaud, Mikio Sato, Moduli scheme, Moduli space, Montpellier, Motive (algebraic geometry), N-group (category theory), Nakai conjecture, Nansen passport, Nicolae Popescu, Nicolas Bourbaki, Nisnevich topology, Noncommutative algebraic geometry, November 13, Nuclear operator, Nuclear space, Open science, Orlicz–Pettis theorem, Oscar Zariski, P-adic Hodge theory, Per Enflo, Perfect complex, Pierre Berthelot, Pierre Cartier (mathematician), Pierre Deligne, Pierre Gabriel, Pierre Samuel, Pierre Schapira (mathematician), Proper morphism, Pseudo-abelian category, Purity (algebraic geometry), Pursuing Stacks, Quasi-finite morphism, Quot scheme, Ramanujam–Samuel theorem, Reductive group, Regular embedding, Representation theory, Riemann–Roch theorem, Rieucros Camp, Rigid analytic space, Rigid category, Ring theory, Robin Hartshorne, Ronald Brown (mathematician), Sascha Schapiro, Séminaire de Géométrie Algébrique du Bois Marie, Séminaire Nicolas Bourbaki (1950–59), Séminaire Nicolas Bourbaki (1960–69), Scheme (mathematics), Schlessinger's theorem, Schwartz space, Seifert–van Kampen theorem, Semi-simplicity, Semistable abelian variety, Serre duality, Sheaf (mathematics), Sheaf cohomology, Shreeram Shankar Abhyankar, Sieve (category theory), Simplicial set, Six operations, Standard conjectures on algebraic cycles, Subfunctor, Subobject classifier, Tannaka–Krein duality, Tannakian formalism, Tarski–Grothendieck set theory, The Story of Maths, Timeline of category theory and related mathematics, Timeline of mathematics, Topological K-theory, Topos, Triangle group, Triangulated category, Univalent foundations, University of Montpellier, University of São Paulo, Verdier duality, Vladimir Voevodsky, Weil conjectures, William Lawvere, William Messing, Yoneda lemma, Yuri Manin, Zariski topology, Zoghman Mebkhout, 1928, 1928 in Germany, 1928 in science, 1966 in science, 2-group, 2014, 2014 in Europe, 2014 in Germany, 20th century in science, 57 (number). Expand index (224 more) »
Abelian category
In mathematics, an abelian category is a category in which morphisms and objects can be added and in which kernels and cokernels exist and have desirable properties.
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Absolute Galois group
In mathematics, the absolute Galois group GK of a field K is the Galois group of Ksep over K, where Ksep is a separable closure of K. Alternatively it is the group of all automorphisms of the algebraic closure of K that fix K. The absolute Galois group is well-defined up to inner automorphism.
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Accessible category
The theory of accessible categories is a part of mathematics, specifically of category theory.
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Adjoint functors
In mathematics, specifically category theory, adjunction is a possible relationship between two functors.
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Affine space
In mathematics, an affine space is a geometric structure that generalizes 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.
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Alexander
Alexander is a common male given name, and a less common surname.
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Algebraic cycle
In mathematics, an algebraic cycle on an algebraic variety V is, roughly speaking, a homology class on V that is represented by a linear combination of subvarieties of V. Therefore, the algebraic cycles on V are the part of the algebraic topology of V that is directly accessible in algebraic geometry.
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Algebraic differential equation
In mathematics, an algebraic differential equation is a differential equation that can be expressed by means of differential algebra.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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Algebraic geometry and analytic geometry
In mathematics, algebraic geometry and analytic geometry are two closely related subjects.
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Algebraic K-theory
Algebraic K-theory is a subject area in mathematics with connections to geometry, topology, ring theory, and number theory.
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Algebraic space
In mathematics, algebraic spaces form a generalization of the schemes of algebraic geometry, introduced by for use in deformation theory.
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Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
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Algebraic torus
In mathematics, an algebraic torus is a type of commutative affine algebraic group.
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Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
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Ample line bundle
In algebraic geometry, a very ample line bundle is one with enough global sections to set up an embedding of its base variety or manifold M into projective space.
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Anabelian geometry
Anabelian geometry is a theory in number theory, which describes the way to which algebraic fundamental group G of a certain arithmetic variety V, or some related geometric object, can help to restore V. First traditional conjectures, originating from Alexander Grothendieck and introduced in Esquisse d'un Programme were about how topological homomorphisms between two groups of two hyperbolic curves over number fields correspond to maps between the curves.
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Anarchism in France
Anarchism in France can trace its roots to thinker Pierre-Joseph Proudhon, who grew up during the Restoration and was the first self-described anarchist.
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André Joyal
André Joyal (born 1943) is a professor of mathematics at the Université du Québec à Montréal who works on category theory.
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André Weil
André Weil (6 May 1906 – 6 August 1998) was an influential French mathematician of the 20th century, known for his foundational work in number theory, algebraic geometry.
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Angus Macintyre
Angus John Macintyre FRS, FRSE (born 1941) is a British mathematician and logician known for his work in Model theory, logic, and their applications in algebra, algebraic geometry, and number theory.
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Approximation property
In mathematics, specifically functional analysis, a Banach space is said to have the approximation property (AP), if every compact operator is a limit of finite-rank operators.
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Arithmetic zeta function
In mathematics, the arithmetic zeta function is a zeta function associated with a scheme of finite type over integers.
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Ax–Grothendieck theorem
In mathematics, the Ax–Grothendieck theorem is a result about injectivity and surjectivity of polynomials that was proved independently by James Ax and Alexander Grothendieck.
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Azumaya algebra
In mathematics, an Azumaya algebra is a generalization of central simple algebras to R-algebras where R need not be a field.
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∞-topos
In mathematics, an ∞-topos is, roughly, an ∞-category such that its objects behave like sheaves of spaces with some choice of Grothendieck topology; in other words, it gives an intrinsic notion of sheaves without reference to an external space.
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École normale supérieure (Paris)
The École normale supérieure (also known as Normale sup', Ulm, ENS Paris, l'École and most often just as ENS) is one of the most selective and prestigious French grandes écoles (higher education establishment outside the framework of the public university system) and a constituent college of Université PSL.
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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.
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Émile Picard Medal
The Émile Picard Medal (or Médaille Émile Picard) is a medal named for Émile Picard awarded every 6 years to an outstanding mathematician by the Institut de France, Académie des sciences.
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Étale cohomology
In mathematics, the étale cohomology groups of an algebraic variety or scheme are algebraic analogues of the usual cohomology groups with finite coefficients of a topological space, introduced by Grothendieck in order to prove the Weil conjectures.
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Étale fundamental group
The étale or algebraic fundamental group is an analogue in algebraic geometry, for schemes, of the usual fundamental group of topological spaces.
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Étale topology
In algebraic geometry, the étale topology is a Grothendieck topology on the category of schemes which has properties similar to the Euclidean topology, but unlike the Euclidean topology, it is also defined in positive characteristic.
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Île de la Jatte
The Île de la Jatte or Île de la Grande Jatte is an island in the river Seine, located in the department of Hauts-de-Seine, and shared between the two communes of Neuilly-sur-Seine and Levallois.
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Banach space
In mathematics, more specifically in functional analysis, a Banach space (pronounced) is a complete normed vector space.
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Barry Mazur
Barry Charles Mazur (born December 19, 1937) is an American mathematician and a Gerhard Gade University Professor at Harvard University.
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Beck's monadicity theorem
In category theory, a branch of mathematics, Beck's monadicity theorem gives a criterion that characterises monadic functors, introduced by in about 1964.
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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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Brieskorn–Grothendieck resolution
In mathematics, a Brieskorn–Grothendieck resolution is a resolution conjectured by Alexander Grothendieck, that in particular gives a resolution of the universal deformation of a Kleinian singularity.
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Bundle of principal parts
In algebraic geometry, given a line bundle L on a smooth variety X, the bundle of n-th order principal parts of L is a vector bundle of rank n + 1 that, roughly, parametrizes n-th order Taylor expansions of sections of L.
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C. P. Ramanujam
Chakravarthi Padmanabhan Ramanujam (9 January 1938 – 27 October 1974) was an Indian mathematician who worked in the fields of number theory and algebraic geometry.
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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.
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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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Claude Chevalley
Claude Chevalley (11 February 1909 – 28 June 1984) was a French mathematician who made important contributions to number theory, algebraic geometry, class field theory, finite group theory, and the theory of algebraic groups.
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Coherent sheaf cohomology
In mathematics, especially in algebraic geometry and the theory of complex manifolds, coherent sheaf cohomology is a technique for producing functions with specified properties.
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Cohomology
In mathematics, specifically in homology theory and algebraic topology, cohomology is a general term for a sequence of abelian groups associated to a topological space, often defined from a cochain complex.
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Colin McLarty
Colin McLarty is an American logician whose publications have ranged widely in philosophy and the foundations of mathematics, as well as in the history of science and of mathematics.
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Commutative algebra
Commutative algebra is the branch of algebra that studies commutative rings, their ideals, and modules over such rings.
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Connection (mathematics)
In geometry, the notion of a connection makes precise the idea of transporting data along a curve or family of curves in a parallel and consistent manner.
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Constructible set (topology)
In topology, a constructible set in a topological space is a finite union of locally closed sets.
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Cotangent complex
In mathematics the cotangent complex is roughly a universal linearization of a morphism of geometric or algebraic objects.
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Crafoord Prize
The Crafoord Prize is an annual science prize established in 1980 by Holger Crafoord, a Swedish industrialist, and his wife Anna-Greta Crafoord.
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Crystalline cohomology
In mathematics, crystalline cohomology is a Weil cohomology theory for schemes X over a base field k. Its values Hn(X/W) are modules over the ring W of Witt vectors over k. It was introduced by and developed by.
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Cyclic homology
In noncommutative geometry and related branches of mathematics, cyclic homology and cyclic cohomology are certain (co)homology theories for associative algebras which generalize the de Rham (co)homology of manifolds.
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D-module
In mathematics, a D-module is a module over a ring D of differential operators.
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Daniel Quillen
Daniel Gray "Dan" Quillen (June 22, 1940 – April 30, 2011) was an American mathematician.
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Dévissage
In algebraic geometry, dévissage is a technique introduced by Alexander Grothendieck for proving statements about coherent sheaves on noetherian schemes.
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Deaths in November 2014
The following is a list of notable deaths in November 2014.
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Deformation theory
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 vector of small quantities.
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Delta-functor
In homological algebra, a δ-functor between two abelian categories A and B is a collection of functors from A to B together with a collection of morphisms that satisfy properties generalising those of derived functors.
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Derivator
In mathematics, derivators are a proposed new framework for homological algebra and various generalisations.
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Derived category
In mathematics, the derived category D(A) of an abelian category A is a construction of homological algebra introduced to refine and in a certain sense to simplify the theory of derived functors defined on A. The construction proceeds on the basis that the objects of D(A) should be chain complexes in A, with two such chain complexes considered isomorphic when there is a chain map that induces an isomorphism on the level of homology of the chain complexes.
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Descent (mathematics)
In mathematics, the idea of descent extends the intuitive idea of 'gluing' in topology.
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Dessin d'enfant
In mathematics, a dessin d'enfant is a type of graph embedding used to study Riemann surfaces and to provide combinatorial invariants for the action of the absolute Galois group of the rational numbers.
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Dieudonné module
In mathematics, a Dieudonné module introduced by, is a module over the non-commutative Dieudonné ring, which is generated over the ring of Witt vectors by two special endomorphisms F and V called the Frobenius and Verschiebung operators.
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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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Dolbeault cohomology
In mathematics, in particular in algebraic geometry and differential geometry, Dolbeault cohomology (named after Pierre Dolbeault) is an analog of de Rham cohomology for complex manifolds.
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Dunford–Pettis property
In functional analysis, the Dunford–Pettis property, named after Nelson Dunford and B. J. Pettis, is a property of a Banach space stating that all weakly compact operators from this space into another Banach space are completely continuous.
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Dvoretzky's theorem
In mathematics, Dvoretzky's theorem is an important structural theorem about normed vector spaces proved by Aryeh Dvoretzky in the early 1960s, answering a question of Alexander Grothendieck.
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Element (category theory)
In category theory, the concept of an element, or a point, generalizes the more usual set theoretic concept of an element of a set to an object of any category.
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Esquisse d'un Programme
"Esquisse d'un Programme" (Sketch of a Programme) is a famous proposal for long-term mathematical research made by the German-born, French mathematician Alexander Grothendieck in 1984.
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Excellent ring
In commutative algebra, a quasi-excellent ring is a Noetherian commutative ring that behaves well with respect to the operation of completion, and is called an excellent ring if it is also universally catenary.
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Exceptional inverse image functor
In mathematics, more specifically sheaf theory, a branch of topology and algebraic geometry, the exceptional inverse image functor is the fourth and most sophisticated in a series of image functors for sheaves.
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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 of definition
In mathematics, the field of definition of an algebraic variety V is essentially the smallest field to which the coefficients of the polynomials defining V can belong.
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Fields Medal
The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years.
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Finite morphism
In algebraic geometry, a morphism f: X → Y of schemes is a finite morphism if Y has an open cover by affine schemes such that for each i, is an open affine subscheme Spec Ai, and the restriction of f to Ui, which induces a ring homomorphism makes Ai a finitely generated module over Bi.
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Fondements de la Géometrie Algébrique
Fondements de la Géometrie Algébrique (FGA) is a book that collected together seminar notes of Alexander Grothendieck.
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Formally smooth map
In algebraic geometry and commutative algebra, a ring homomorphism f:A\to B is called formally smooth (from French: Formellement lisse) if it satisfies the following infinitesimal lifting property: Suppose B is given the structure of an A-algebra via the map f. Given a commutative A-algebra, C, and a nilpotent ideal N\subseteq C, any A-algebra homomorphism B\to C/N may be lifted to an A-algebra map B \to C. If moreover any such lifting is unique, then f is said to be formally étale.
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Foundations of Algebraic Geometry
Foundations of Algebraic Geometry is a book by that develops algebraic geometry over fields of any characteristic.
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Fredholm kernel
In mathematics, a Fredholm kernel is a certain type of a kernel on a Banach space, associated with nuclear operators on the Banach space.
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French mathematical seminars
French mathematical seminars have been an important type of institution combining research and exposition, active since the beginning of the twentieth century.
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Fundamental group
In the mathematical field of algebraic topology, the fundamental group is a mathematical group associated to any given pointed topological space that provides a way to determine when two paths, starting and ending at a fixed base point, can be continuously deformed into each other.
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Fundamental group scheme
In mathematics, the fundamental group scheme is a group scheme canonically attached to a scheme over a Dedekind scheme (e.g. the spectrum of a field or the spectrum of a discrete valuation ring).
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G-ring
In commutative algebra, a G-ring or Grothendieck ring is a Noetherian ring such that the map of any of its local rings to the completion is regular (defined below).
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Galois extension
In mathematics, a Galois extension is an algebraic field extension E/F that is normal and separable; or equivalently, E/F is algebraic, and the field fixed by the automorphism group Aut(E/F) is precisely the base field F. The significance of being a Galois extension is that the extension has a Galois group and obeys the fundamental theorem of Galois theory.
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Galois module
In mathematics, a Galois module is a ''G''-module, with G being the Galois group of some extension of fields.
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Galois theory
In the field of algebra within mathematics, Galois theory, provides a connection between field theory and group theory.
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Generic flatness
In algebraic geometry and commutative algebra, the theorems of generic flatness and generic freeness state that under certain hypotheses, a sheaf of modules on a scheme is flat or free.
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Geometric invariant theory
In mathematics Geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli spaces.
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Geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.
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George Mackey
George Whitelaw Mackey (February 1, 1916 – March 15, 2006) was an American mathematician.
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Gerbe
In mathematics, a gerbe is a construct in homological algebra and topology.
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Globular set
In category theory, a branch of mathematics, a globular set is a higher-dimensional generalization of a directed graph.
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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 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.
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Glossary of category theory
This is a glossary of properties and concepts in category theory in 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.
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Glossary of commutative algebra
This is a glossary of commutative algebra.
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Grothendieck category
In mathematics, a Grothendieck category is a certain kind of abelian category, introduced in Alexander Grothendieck's Tôhoku paper of 1957.
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Grothendieck construction
The Grothendieck construction (named after Alexander Grothendieck) is a construction used in the mathematical field of category theory.
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Grothendieck group
In mathematics, the Grothendieck group construction in abstract algebra constructs an abelian group from a commutative monoid M in the most universal way in the sense that any abelian group containing a homomorphic image of M will also contain a homomorphic image of the Grothendieck group of M. The Grothendieck group construction takes its name from the more general construction in category theory, introduced by Alexander Grothendieck in his fundamental work of the mid-1950s that resulted in the development of K-theory, which led to his proof of the Grothendieck–Riemann–Roch theorem.
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Grothendieck inequality
In mathematics, the Grothendieck inequality states that there is a universal constant k with the following property.
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Grothendieck space
In mathematics, a Grothendieck space, named after Alexander Grothendieck, is a Banach space X in which every weakly* convergent sequence in the dual space X* converges with respect to the weak topology of X*.
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Grothendieck topology
In category theory, a branch of mathematics, a Grothendieck topology is a structure on a category C which makes the objects of C act like the open sets of a topological space.
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Grothendieck universe
In mathematics, a Grothendieck universe is a set U with the following properties.
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Grothendieck's Galois theory
In mathematics, Grothendieck's Galois theory is an abstract approach to the Galois theory of fields, developed around 1960 to provide a way to study the fundamental group of algebraic topology in the setting of algebraic geometry.
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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.
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Grothendieck's Tôhoku paper
The article "Sur quelques points d'algèbre homologique" by Alexander Grothendieck, now often referred to as the Tôhoku paper, was published in 1957 in the Tôhoku Mathematical Journal.
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Grothendieck–Katz p-curvature conjecture
In mathematics, the Grothendieck–Katz p-curvature conjecture is a local-global principle for linear ordinary differential equations, related to differential Galois theory and in a loose sense analogous to the result in the Chebotarev density theorem considered as the polynomial case.
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Grothendieck–Riemann–Roch theorem
In mathematics, specifically in algebraic geometry, the Grothendieck–Riemann–Roch theorem is a far-reaching result on coherent cohomology.
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Grothendieck–Teichmüller group
In mathematics, the Grothendieck–Teichmüller group GT is a group closely related to (and possibly equal to) the absolute Galois group of the rational numbers.
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Group scheme
In mathematics, a group scheme is a type of algebro-geometric object equipped with a composition law.
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Henri Cartan
Henri Paul Cartan (July 8, 1904 – August 13, 2008) was a French mathematician with substantial contributions in algebraic topology.
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Hilbert's problems
Hilbert's problems are twenty-three problems in mathematics published by German mathematician David Hilbert in 1900.
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History of geometry
Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") arose as the field of knowledge dealing with spatial relationships.
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History of mathematical notation
The history of mathematical notation includes the commencement, progress, and cultural diffusion of mathematical symbols and the conflict of the methods of notation confronted in a notation's move to popularity or inconspicuousness.
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History of mathematics
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
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History of topos theory
This page gives some very general background to the mathematical idea of topos.
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Hoàng Xuân Sính
Hoàng Xuân Sính is a Vietnamese mathematician, a student of Grothendieck, the first female mathematician in Vietnam, the founder of Thang Long University, and the recipient of the Ordre des Palmes Académiques.
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Hodge structure
In mathematics, a Hodge structure, named after W. V. D. Hodge, is an algebraic structure at the level of linear algebra, similar to the one that Hodge theory gives to the cohomology groups of a smooth and compact Kähler manifold.
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Homological algebra
Homological algebra is the branch of mathematics that studies homology in a general algebraic setting.
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Homotopy hypothesis
In category theory, a branch of mathematics, Grothendieck's homotopy hypothesis states that the ∞-groupoids are equivalent to the topological spaces.
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Hyperfunction
In mathematics, hyperfunctions are generalizations of functions, as a 'jump' from one holomorphic function to another at a boundary, and can be thought of informally as distributions of infinite order.
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Inaccessible cardinal
In set theory, an uncountable cardinal is inaccessible if it cannot be obtained from smaller cardinals by the usual operations of cardinal arithmetic.
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Injective sheaf
In mathematics, injective sheaves of abelian groups are used to construct the resolutions needed to define sheaf cohomology (and other derived functors, such as sheaf Ext).
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Institut des Hautes Études Scientifiques
The Institut des hautes études scientifiques (IHÉS; English: Institute of Advanced Scientific Studies) is a French institute supporting advanced research in mathematics and theoretical physics.
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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.
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Internment camps in France
There were internment camps and concentration camps in France before, during and after World War II.
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Inverse limit
In mathematics, the inverse limit (also called the projective limit or limit) is a construction that allows one to "glue together" several related objects, the precise manner of the gluing process being specified by morphisms between the objects.
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Inverse system
In mathematics, an inverse system in a category C is a functor from a small cofiltered category I to C. An inverse system is sometimes called a pro-object in C. The dual concept is a direct system.
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Λ-ring
In algebra, a λ-ring or lambda ring is a commutative ring together with some operations λn on it that behave like the exterior powers of vector spaces.
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Jean Dieudonné
Jean Alexandre Eugène Dieudonné (1 July 1906 – 29 November 1992) was a French mathematician, notable for research in abstract algebra, algebraic geometry, and functional analysis, for close involvement with the Nicolas Bourbaki pseudonymous group and the Éléments de géométrie algébrique project of Alexander Grothendieck, and as a historian of mathematics, particularly in the fields of functional analysis and algebraic topology.
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Jean Giraud (mathematician)
Jean Giraud (2 February 1936 – 27 or 28 March 2007), Philippe Gillet, ENS Info 70, April 2007.
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Jean-Louis Verdier
Jean-Louis Verdier (2 February 1935 – 25 August 1989) was a French mathematician who worked, under the guidance of Alexander Grothendieck, on derived categories and Verdier duality.
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Jean-Pierre Serre
Jean-Pierre Serre (born 15 September 1926) is a French mathematician who has made contributions to algebraic topology, algebraic geometry, and algebraic number theory.
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John Edensor Littlewood
John Edensor Littlewood FRS LLD (9 June 1885 – 6 September 1977) was an English mathematician.
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K-theory
In mathematics, K-theory is, roughly speaking, the study of a ring generated by vector bundles over a topological space or scheme.
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Künneth theorem
In mathematics, especially in homological algebra and algebraic topology, a Künneth theorem, also called a Künneth formula, is a statement relating the homology of two objects to the homology of their product.
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Kunihiko Kodaira
was a Japanese mathematician known for distinguished work in algebraic geometry and the theory of complex manifolds, and as the founder of the Japanese school of algebraic geometers.
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Lasserre, Ariège
Lasserre is a commune in the Ariège department in southwestern France.
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Laurent Schwartz
Laurent-Moïse Schwartz (5 March 1915 – 4 July 2002) was a French mathematician.
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Léon Motchane
Léon Motchane (19 June 1900 – 17 January 1990) was a French industrialist and mathematician and the founder of the Institut des Hautes Études Scientifiques in Bures-sur-Yvette.
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Le Chambon-sur-Lignon
Le Chambon-sur-Lignon (Auvergnat: Lo Chambon) is a commune in the Haute-Loire department in south-central France.
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Le Collège-Lycée Cévenol International
The Collège Cévenol—later known as Le Collège-Lycée Cévenol International—was a unique and historic international secondary school located in Le Chambon-sur-Lignon, in the département of Haute-Loire, France.
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Lefschetz hyperplane theorem
In mathematics, specifically in algebraic geometry and algebraic topology, the Lefschetz hyperplane theorem is a precise statement of certain relations between the shape of an algebraic variety and the shape of its subvarieties.
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Leila Schneps
Leila Schneps (born December 22, 1961) is an American mathematician, living in France, employed by Centre national de la recherche scientifique, and based at the Jussieu of Pierre and Marie Curie University, France, where she specializes in number theory.
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Leray spectral sequence
In mathematics, the Leray spectral sequence was a pioneering example in homological algebra, introduced in 1946 by Jean Leray.
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List of algebraic geometry topics
This is a list of algebraic geometry topics, by Wikipedia page.
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List of École normale supérieure people
Here follows a list of notable alumni and faculty of the École normale supérieure.
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List of Brazilian scientists
This is a list of Brazilian scientists, those born in Brazil or who have established citizenship or residency there.
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List of countries by number of Fields Medallists
This article includes a list of countries by number of Fields Medal winners.
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List of Fields Medal winners by university affiliation
The following list comprehensively shows Fields Medal winners by university affiliations since 1936 (as of 2017, 56 winners in total).
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List of French scientists
This is a list of notable French scientists.
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List of geometers
A geometer is a mathematician whose area of study is geometry.
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List of German inventors and discoverers
---- This is a list of German inventors and discoverers.
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List of Holocaust survivors
The people on this list are or were survivors of Nazi Germany's attempt to exterminate the Jews in Europe before and during World War II.
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List of important publications in mathematics
This is a list of important publications in mathematics, organized by field.
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List of International Congresses of Mathematicians Plenary and Invited Speakers
This is a list of International Congresses of Mathematicians Plenary and Invited Speakers.
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List of Jewish mathematicians
This list of Jewish mathematicians includes mathematicians who are or were verifiably Jewish or of Jewish descent.
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List of mathematicians (G)
No description.
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List of Occitans
This is a non-exhaustive list of people who were born in the Occitania historical territory (although it is difficult to know the exact boundaries), or notable people from other regions of France or Europe with Occitan roots, or notable people from other regions of France or Europe who have other significant links with the historical region.
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List of people by Erdős number
Paul Erdős (1913–1996) was the most prolifically published mathematician of all time.
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List of recluses
This is a list of notable recluses.
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List of refugees
This is a list of prominent people who are or were refugees.
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List of things named after Alexander Grothendieck
The mathematician Alexander Grothendieck (1928–2014) is the eponym of many things.
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Local cohomology
In algebraic geometry, local cohomology is an analog of relative cohomology.
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Local zeta-function
In number theory, the local zeta function Z(V,s) (sometimes called the congruent zeta function) is defined as where N_m is the number of points of V defined over the degree m extension \mathbf_ of \mathbf_q, and V is a non-singular n-dimensional projective algebraic variety over the field \mathbf_q with q elements.
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Localizing subcategory
In mathematics, Serre and localizing subcategories form important classes of subcategories of an abelian category.
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Lorenzo Ramero
Lorenzo Ramero is an Italian mathematician living in France, specialized in algebraic and arithmetic geometry.
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Luc Illusie
Luc Illusie (born 1940) is a French mathematician, specializing in algebraic geometry.
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March 1928
The following events occurred in March 1928.
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March 28
No description.
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Masaki Kashiwara
is a Japanese mathematician.
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Max Karoubi
Max Karoubi is a French mathematician who works on K-theory and who founded the first European Congress of Mathematics.
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Mende, Lozère
Mende is a commune and prefecture of the department of Lozère and of the region of Occitanie in southern France.
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Michael Atiyah
Sir Michael Francis Atiyah (born 22 April 1929) is an English mathematician specialising in geometry.
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Michel Demazure
Michel Demazure (born 2 March 1937) is a French mathematician.
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Michel Raynaud
Michel Raynaud (16 June 1938 – 10 March 2018) was a French mathematician working in algebraic geometry.
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Mikio Sato
is a Japanese mathematician, who started the field of algebraic analysis.
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Moduli scheme
In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck.
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Moduli space
In 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.
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Montpellier
Montpellier (Montpelhièr) is a city in southern France.
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Motive (algebraic geometry)
In algebraic geometry, a motive (or sometimes motif, following French usage) denotes 'some essential part of an algebraic variety'.
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N-group (category theory)
In mathematics, an n-group, or n-dimensional higher group, is a special kind of ''n''-category that generalises the concept of group to higher-dimensional algebra.
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Nakai conjecture
In mathematics, the Nakai conjecture is an unproven characterization of smooth algebraic varieties, conjectured by Japanese mathematician Yoshikazu Nakai in 1961.
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Nansen passport
Nansen passports, originally and officially stateless persons passports, were internationally recognized refugee travel documents from 1922 to 1938, first issued by the League of Nations to stateless refugees.
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Nicolae Popescu
Nicolae Popescu, Ph.D., D.Phil. (22 September 1937 – 29 July 2010) was a Romanian mathematician and professor at the University of Bucharest.
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Nicolas Bourbaki
Nicolas Bourbaki is the collective pseudonym under which a group of (mainly French) 20th-century mathematicians, with the aim of reformulating mathematics on an extremely abstract and formal but self-contained basis, wrote a series of books beginning in 1935.
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Nisnevich topology
In algebraic geometry, the Nisnevich topology, sometimes called the completely decomposed topology, is a Grothendieck topology on the category of schemes which has been used in algebraic K-theory, A¹ homotopy theory, and the theory of motives.
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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).
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November 13
No description.
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Nuclear operator
In mathematics, a nuclear operator is a compact operator for which a trace may be defined, such that the trace is finite and independent of the choice of basis (at least on well behaved spaces; there are some spaces on which nuclear operators do not have a trace).
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Nuclear space
In mathematics, a nuclear space is a topological vector space with many of the good properties of finite-dimensional vector spaces.
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Open science
Open science is the movement to make scientific research, data and dissemination accessible to all levels of an inquiring society, amateur or professional.
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Orlicz–Pettis theorem
A theorem in functional analysis concerning convergent series (Orlicz) or, equivalently, countable additivity of measures (Pettis) with values in abstract spaces.
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Oscar Zariski
Oscar Zariski (born Oscher Zaritsky (О́скар Зари́сский; April 24, 1899 – July 4, 1986) was a Russian-born American mathematician and one of the most influential algebraic geometers of the 20th century.
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P-adic Hodge theory
In mathematics, p-adic Hodge theory is a theory that provides a way to classify and study ''p''-adic Galois representations of characteristic 0 local fields with residual characteristic p (such as '''Q'''''p'').
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Per Enflo
Per H. Enflo (born 20 May 1944) is a Swedish mathematician working primarily in functional analysis, a field in which he solved problems that had been considered fundamental.
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Perfect complex
In algebra, a perfect complex of modules over a commutative ring A is an object in the derived category of A-modules that is quasi-isomorphic to a bounded complex of finite projective A-modules.
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Pierre Berthelot
Pierre Berthelot is a mathematician at the University of Rennes.
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Pierre Cartier (mathematician)
Pierre Emile Cartier (born 10 June 1932) is a mathematician.
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Pierre Deligne
Pierre René, Viscount Deligne (born 3 October 1944) is a Belgian mathematician.
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Pierre Gabriel
Pierre Gabriel (1 August 1933 – 24 November 2015), also known as Peter Gabriel, was a French mathematician at the universities of Strasbourg (1962-1970), Bonn (1970-1974) and Zürich (1974-1998) who worked on category theory, algebraic groups, and representation theory of algebras.
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Pierre Samuel
Pierre Samuel (12 September 1921 – 23 August 2009 Obituary of Pierre Samuel (LeMonde)) was a French mathematician, known for his work in commutative algebra and its applications to algebraic geometry.
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Pierre Schapira (mathematician)
Pierre Schapira (born April 28, 1943) is a French mathematician.
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Proper morphism
In algebraic geometry, a proper morphism between schemes is an analog of a proper map between complex analytic spaces.
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Pseudo-abelian category
In mathematics, specifically in category theory, a pseudo-abelian category is a category that is preadditive and is such that every idempotent has a kernel.
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Purity (algebraic geometry)
In the mathematical field of algebraic geometry, purity is a theme covering a number of results and conjectures, which collectively address the question of proving that "when something happens, it happens in a particular codimension".
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Pursuing Stacks
Pursuing Stacks (À la Poursuite des Champs) is an influential 1983 mathematical manuscript by Alexander Grothendieck.
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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.
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Quot scheme
In algebraic geometry, the Quot scheme is a scheme parametrizing locally free sheaves on a projective scheme.
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Ramanujam–Samuel theorem
In algebraic geometry, the Ramanujam–Samuel theorem gives conditions for a divisor of a local ring to be principal.
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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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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.
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Representation theory
Representation theory is a branch of mathematics that studies abstract algebraic structures by representing their elements as linear transformations of vector spaces, and studies modules over these abstract algebraic structures.
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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 zeroes and allowed poles.
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Rieucros Camp
The Rieucros Camp was an internment camp on a forested hillside near Mende in the French department of Lozère that operated from January 1939 to February 1942.
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Rigid analytic space
In mathematics, a rigid analytic space is an analogue of a complex analytic space over a nonarchimedean field.
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Rigid category
In category theory, a branch of mathematics, a rigid category is a monoidal category where every object is rigid, that is, has a dual X* (the internal Hom) and a morphism 1 → X ⊗ X* satisfying natural conditions.
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Ring theory
In algebra, ring theory is the study of rings—algebraic structures in which addition and multiplication are defined and have similar properties to those operations defined for the integers.
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Robin Hartshorne
Robin Cope Hartshorne (born March 15, 1938) is an American mathematician.
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Ronald Brown (mathematician)
Ronald Brown is an English mathematician.
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Sascha Schapiro
Alexander "Sascha" Schapiro (Александр Шапиро; – 1942), also known by the noms de guerre Alexander Tanarov, Sascha Piotr, and Sergei, was an anarchist revolutionary and father of eminent 20th century mathematician Alexander Grothendieck.
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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.
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Séminaire Nicolas Bourbaki (1950–59)
Continuation of the Séminaire Nicolas Bourbaki programme, for the 1950s.
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Séminaire Nicolas Bourbaki (1960–69)
Continuation of the Séminaire Nicolas Bourbaki programme, for the 1960s.
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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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Schlessinger's theorem
In algebra, Schlessinger's theorem is a theorem in deformation theory introduced by that gives conditions for a functor of artinian local rings to be pro-representable, refining an earlier theorem of Grothendieck.
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Schwartz space
In mathematics, Schwartz space is the function space of all functions whose derivatives are rapidly decreasing (defined rigorously below).
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Seifert–van Kampen theorem
In mathematics, the Seifert–van Kampen theorem of algebraic topology (named after Herbert Seifert and Egbert van Kampen), sometimes just called van Kampen's theorem, expresses the structure of the fundamental group of a topological space X in terms of the fundamental groups of two open, path-connected subspaces that cover X. It can therefore be used for computations of the fundamental group of spaces that are constructed out of simpler ones.
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Semi-simplicity
In mathematics, semi-simplicity is a widespread concept in disciplines such as linear algebra, abstract algebra, representation theory, category theory, and algebraic geometry.
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Semistable abelian variety
In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces at the primes of the field.
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Serre duality
In algebraic geometry, a branch of mathematics, Serre duality is a duality present on non-singular projective algebraic varieties V of dimension n (and in greater generality for vector bundles and further, for coherent sheaves).
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Sheaf (mathematics)
In mathematics, a sheaf is a tool for systematically tracking locally defined data attached to the open sets of a topological space.
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Sheaf cohomology
In mathematics, sheaf cohomology is the application of homological algebra to analyze the global sections of a sheaf on a topological space.
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Shreeram Shankar Abhyankar
Shreeram Shankar Abhyankar (22 July 1930 – 2 November 2012) was an Indian American mathematician known for his contributions to algebraic geometry.
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Sieve (category theory)
In category theory, a branch of mathematics, a sieve is a way of choosing arrows with a common codomain.
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Simplicial set
In mathematics, a simplicial set is an object made up of "simplices" in a specific way.
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Six operations
In mathematics, Grothendieck's six operations, named after Alexander Grothendieck, is a formalism in homological algebra.
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Standard conjectures on algebraic cycles
In mathematics, the standard conjectures about algebraic cycles are several conjectures describing the relationship of algebraic cycles and Weil cohomology theories.
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Subfunctor
In category theory, a branch of mathematics, a subfunctor is a special type of functor which is an analogue of a subset.
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Subobject classifier
In category theory, a subobject classifier is a special object Ω of a category such that, intuitively, the subobjects of any object X in the category correspond to the morphisms from X to Ω. In typical examples, that morphism assigns "true" to the elements of the subobject and "false" to the other elements of X. Therefore a subobject classifier is also known as a "truth value object" and the concept is widely used in the categorical description of logic.
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Tannaka–Krein duality
In mathematics, Tannaka–Krein duality theory concerns the interaction of a compact topological group and its category of linear representations.
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Tannakian formalism
In mathematics, a tannakian category is a particular kind of monoidal category C, equipped with some extra structure relative to a given field K. The role of such categories C is to approximate, in some sense, the category of linear representations of an algebraic group G defined over K. A number of major applications of the theory have been made, or might be made in pursuit of some of the central conjectures of contemporary algebraic geometry and number theory.
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Tarski–Grothendieck set theory
Tarski–Grothendieck set theory (TG, named after mathematicians Alfred Tarski and Alexander Grothendieck) is an axiomatic set theory.
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The Story of Maths
The Story of Maths is a four-part British television series outlining aspects of the history of mathematics.
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Timeline of category theory and related mathematics
This is a timeline of category theory and related mathematics.
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Timeline of mathematics
This is a timeline of pure and applied mathematics history.
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Topological K-theory
In mathematics, topological -theory is a branch of algebraic topology.
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Topos
In mathematics, a topos (plural topoi or, or toposes) is a category that behaves like the category of sheaves of sets on a topological space (or more generally: on a site).
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Triangle group
In mathematics, a triangle group is a group that can be realized geometrically by sequences of reflections across the sides of a triangle.
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Triangulated category
In mathematics, a triangulated category is a category together with the additional structure of a "translation functor" and a class of "distinguished triangles".
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Univalent foundations
Univalent foundations are an approach to the foundations of mathematics in which mathematical structures are built out of objects called types.
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University of Montpellier
The University of Montpellier (Université de Montpellier) is a French public research university in Montpellier in south-east of France.
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University of São Paulo
No description.
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Verdier duality
In mathematics, Verdier duality is a duality in sheaf theory that generalizes Poincaré duality for manifolds.
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Vladimir Voevodsky
Vladimir Alexandrovich Voevodsky (Влади́мир Алекса́ндрович Воево́дский, 4 June 1966 – 30 September 2017) was a Russian-American mathematician.
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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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William Lawvere
Francis William Lawvere (born February 9, 1937) is a mathematician known for his work in category theory, topos theory and the philosophy of mathematics.
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William Messing
William Messing is an American mathematician who works in the field of arithmetic algebraic geometry.
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Yoneda lemma
In mathematics, specifically in category theory, the Yoneda lemma is an abstract result on functors of the type morphisms into a fixed object.
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Yuri Manin
Yuri Ivanovitch Manin (Ю́рий Ива́нович Ма́нин; born 1937) is a Soviet/Russian/German CURRICULUM VITAE at Max-Planck-Institut für Mathematik website mathematician, known for work in algebraic geometry and diophantine geometry, and many expository works ranging from mathematical logic to theoretical physics.
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Zariski topology
In algebraic geometry and commutative algebra, the Zariski topology is a topology on algebraic varieties, introduced primarily by Oscar Zariski and later generalized for making the set of prime ideals of a commutative ring a topological space, called the spectrum of the ring.
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Zoghman Mebkhout
Zoghman Mebkhout (born 1949) (مبخوت زغمان) is a French-Algerian mathematician known for his work in algebraic analysis, geometry, and representation theory, more precisely on the theory of D-modules.
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1928
No description.
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1928 in Germany
Events in the year 1928 in Germany.
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1928 in science
The year 1928 in science and technology involved some significant events, listed below.
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1966 in science
The year 1966 in science and technology involved some significant events, listed below.
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2-group
In mathematics, a 2-group, or 2-dimensional higher group, is a certain combination of group and groupoid.
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2014
2014 was designated as.
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2014 in Europe
This is a list of 2014 events that occurred in Europe.
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2014 in Germany
Events in the year 2014 in Germany.
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20th century in science
Science advanced dramatically during the 20th century.
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57 (number)
57 (fifty-seven) is the natural number following 56 and preceding 58.
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Redirects here:
A Grothendieck, Alexander Raddatz, Alexander grothendieck, Alexandre Grothendieck, Grothendieck, Grothendieck, A., Grothendieck, Alexander, Récoltes et semailles, Shurik Grothendieck.
References
[1] https://en.wikipedia.org/wiki/Alexander_Grothendieck
