15 relations: A¹ homotopy theory, Adele ring, Alexander Grothendieck, Algebraic geometry, Algebraic K-theory, Grothendieck topology, Henselian ring, Jean-Pierre Serre, Motive (algebraic geometry), Principal homogeneous space, Residue field, Resolution of singularities, Scheme (mathematics), Spectral sequence, Zariski topology.
A¹ homotopy theory
In algebraic geometry and algebraic topology, a branch of mathematics, homotopy theory is a way to apply the techniques of algebraic topology, specifically homotopy, to algebraic varieties and, more generally, to schemes.
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Adele ring
In mathematics, the adele ring (also adelic ring or ring of adeles) is defined in class field theory, a branch of algebraic number theory.
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Alexander Grothendieck
Alexander Grothendieck (28 March 1928 – 13 November 2014) was a German-born French mathematician who became the leading figure in the creation of modern algebraic geometry.
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Algebraic geometry
Algebraic geometry is a branch of mathematics, classically studying zeros of multivariate polynomials.
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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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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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Henselian ring
In mathematics, a Henselian ring (or Hensel ring) is a local ring in which Hensel's lemma holds.
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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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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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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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Residue field
In mathematics, the residue field is a basic construction in commutative algebra.
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Resolution of singularities
In algebraic geometry, the problem of resolution of singularities asks whether every algebraic variety V has a resolution, a non-singular variety W with a proper birational map W→V.
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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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Spectral sequence
In homological algebra and algebraic topology, a spectral sequence is a means of computing homology groups by taking successive approximations.
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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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