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Media type:
Book
Title:
A1-algebraic topology over a field
Contains:
Introduction -- Unramified sheaves and strongly A¹-invariant sheaves -- Unramified Milnor-Witt K-theories -- Geometric versus canonical transfers -- The Rost-Schmid complex of a strongly A¹-invariant sheaf -- A¹-homotopy sheaves and A¹-homology sheaves -- A¹-coverings, [Pi]A¹1 (Pn) and [Pi]A¹1 (SLn) -- A¹-homotopy and algebraic vector bundles -- The affine B.G. property for the linear groups and the Grassmanian -- The (Affine) B.G. property for simplicial sheaves -- Recollection on obstruction theory.
Description:
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-homotogy sheaves, and sheaves with generalized transfers, as well as to algebraic vector bundles over affine smooth varieties--