A1-Algebraic Topology over a Field

Nonfiction, Science & Nature, Mathematics, Geometry, Algebra
Cover of the book A1-Algebraic Topology over a Field by Fabien Morel, Springer Berlin Heidelberg
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Author: Fabien Morel ISBN: 9783642295140
Publisher: Springer Berlin Heidelberg Publication: July 13, 2012
Imprint: Springer Language: English
Author: Fabien Morel
ISBN: 9783642295140
Publisher: Springer Berlin Heidelberg
Publication: July 13, 2012
Imprint: Springer
Language: English

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-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.

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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-homology sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties.

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