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24 relations: Algebraic geometry, Algebraic K-theory, Algebraic topology, Algebraic variety, Derived category, Fabien Morel, Grothendieck topology, Homotopy, Homotopy category, Lifting property, Mathematics, Milnor conjecture, Model category, Motive (algebraic geometry), Nisnevich topology, Noetherian scheme, Norm residue isomorphism theorem, Publications Mathématiques de l'IHÉS, Scheme (mathematics), Simplex category, Simplicial set, Smooth morphism, Topos, Vladimir Voevodsky.
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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Algebraic topology
Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces.
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Algebraic variety
Algebraic varieties are the central objects of study in algebraic geometry.
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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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Fabien Morel
Fabien Morel (born 22 January 1965 in Reims) is a French algebraic geometer and key developer of A¹ homotopy theory with Vladimir Voevodsky.
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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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Homotopy
In topology, two continuous functions from one topological space to another are called homotopic (from Greek ὁμός homós "same, similar" and τόπος tópos "place") if one can be "continuously deformed" into the other, such a deformation being called a homotopy between the two functions.
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Homotopy category
In mathematics, the homotopy category is a category built from the category of topological spaces which in a sense identifies two spaces that have the same shape.
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Lifting property
In mathematics, in particular in category theory, the lifting property is a property of a pair of morphisms in a category.
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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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Milnor conjecture
In mathematics, the Milnor conjecture was a proposal by of a description of the Milnor K-theory (mod 2) of a general field F with characteristic different from 2, by means of the Galois (or equivalently étale) cohomology of F with coefficients in Z/2Z.
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Model category
In mathematics, particularly in homotopy theory, a model category is a category with distinguished classes of morphisms ('arrows') called 'weak equivalences', 'fibrations' and 'cofibrations'.
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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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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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Noetherian scheme
In algebraic geometry, a noetherian scheme is a scheme that admits a finite covering by open affine subsets \operatorname A_i, A_i noetherian rings.
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Norm residue isomorphism theorem
In mathematics, the norm residue isomorphism theorem is a long-sought result relating Milnor ''K''-theory and Galois cohomology.
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Publications Mathématiques de l'IHÉS
Publications Mathématiques de l'IHÉS is a mathematical journal.
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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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Simplex category
In mathematics, the simplex category (or simplicial category or nonempty finite ordinal category) is the category of non-empty finite ordinals and order preserving maps.
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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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Smooth morphism
In algebraic geometry, a morphism f:X \to S between schemes is said to be smooth if.
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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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Vladimir Voevodsky
Vladimir Alexandrovich Voevodsky (Влади́мир Алекса́ндрович Воево́дский, 4 June 1966 – 30 September 2017) was a Russian-American mathematician.
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Redirects here:
A1 homotopy theory, A¹, Motivic homotopy, Motivic homotopy theory.
References
[1] https://en.wikipedia.org/wiki/A¹_homotopy_theory
