A1-algebraic topology over a field / Fabien Morel

Auteur: Morel, Fabien (1965-) - AuteurType de document: MonographieCollection: Lecture notes in mathematics ; 2052Langue: anglaisPays: AllemagneÉditeur: Berlin : Springer, cop. 2012Description: 1 vol. (X-259 p.) ; 24 cm ISBN: 9783642295133 ; br. Résumé: This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homotopy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties. (Source : Springer).Bibliographie: Bibliogr. p. 255-258. Index. Sujets MSC: 14-02 Algebraic geometry -- Research exposition (monographs, survey articles)
14C35 Algebraic geometry -- Cycles and subschemes -- Applications of methods of algebraic K-theory
14F42 Algebraic geometry -- (Co)homology theory -- Motivic cohomology; motivic homotopy theory
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Bibliogr. p. 255-258. Index

This text deals with A1-homotopy theory over a base field, i.e., with the natural homotopy theory associated to the category of smooth varieties over a field in which the affine line is imposed to be contractible. It is a natural sequel to the foundational paper on A1-homotopy theory written together with V. Voevodsky. Inspired by classical results in algebraic topology, we present new techniques, new results and applications related to the properties and computations of A1-homotopy sheaves, A1-homotopy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties. (Source : Springer)

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