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Mathematics - Algebra | A1-Algebraic Topology over a Field

A1-Algebraic Topology over a Field

Series: Lecture Notes in Mathematics, Vol. 2052

Morel, Fabien

2012, X, 259 p.

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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.

Content Level » Research

Keywords » 14-XX; 19-XX; 55-XX - Algebraic vector bundles - Milnor-Witt K-theory - Motivic homotopy theory - Sheaves with transfers

Related subjects » Algebra - Geometry & Topology

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