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17 relations: Algebraic geometry, Éléments de géométrie algébrique, Derived functor, Descent (mathematics), Flat module, Flat morphism, Fpqc morphism, Galois cohomology, Grothendieck topology, James Milne (mathematician), Mathematics, Michael Artin, Pretopological space, Sheaf (mathematics), Société mathématique de France, Spectrum of a ring, Tate duality.
Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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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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Derived functor
In mathematics, certain functors may be derived to obtain other functors closely related to the original ones.
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Descent (mathematics)
In mathematics, the idea of descent extends the intuitive idea of 'gluing' in topology.
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Flat module
In homological algebra and algebraic geometry, a flat module over a ring R is an R-module M such that taking the tensor product over R with M preserves exact sequences.
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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 → B is called flat, if it is a homomorphism that makes B a flat A-module.
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Fpqc morphism
In algebraic geometry, there are two slightly different definitions of an fpqc morphism, both variations of faithfully flat morphisms.
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Galois cohomology
In mathematics, Galois cohomology is the study of the group cohomology of Galois modules, that is, the application of homological algebra to modules for Galois groups.
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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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James Milne (mathematician)
James S. Milne (born October 10, 1942 in Invercargill, New Zealand) is a New Zealand mathematician working in arithmetic geometry.
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Mathematics
Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.
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Michael Artin
Michael Artin (born 28 June 1934) is an American mathematician and a professor emeritus in the Massachusetts Institute of Technology mathematics department, known for his contributions to algebraic geometry.
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Pretopological space
In general topology, a pretopological space is a generalization of the concept of topological space.
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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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Société mathématique de France
The Société Mathématique de France (SMF) is the main professional society of French mathematicians.
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Spectrum of a ring
In abstract algebra and algebraic geometry, the spectrum of a commutative ring R, denoted by \operatorname(R), is the set of all prime ideals of R. It is commonly augmented with the Zariski topology and with a structure sheaf, turning it into a locally ringed space.
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Tate duality
In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic number field or local field, introduced by and.
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Faithfully flat descent, Flat cohomology, Flat topos, Fppf, Fppf topology, Fpqc topology, Fpqc-topology.
