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Nisnevich topology

Index 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. [1]

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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Redirects here:

L' topology, L′ topology.

References

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

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