A1-Algebraic Topology over a Field

This volume deals with A 1 -homotopy theory over a base field. It is a natural sequel to the foundational paper on A 1 -homotopy theory written together with V. Voevodsky. Inspired by classical algebraic topology, we present new techniques, new results and applications related to A 1 -homotopy sheaves, A 1 -homology sheaves, sheaves with generalized transfers and algebraic vector bundles.

List of contents

1 Introduction.- 2 Unramified sheaves and strongly A1-invariant sheaves.- 3 Unramified Milnor-Witt K-theories.- 4 Geometric versus canonical transfers.- 5 The Rost-Schmid complex of a strongly A1-invariant sheaf.- 6 A1-homotopy sheaves and A1-homology sheaves.- 7 A1-coverings.- 8 A1-homotopy and algebraic vector bundles.- 9 The affine B.G. property for the linear groups and the Grassmanian

Summary

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.

Product details

• Authors: Fabien Morel
• Publisher: Springer, Berlin
• Languages: English
• Product format: Paperback / Softback
• Released: 22.03.2012
• EAN: 9783642295133
• ISBN: 978-3-642-29513-3
• No. of pages: 259
• Dimensions: 153 mm x 17 mm x 237 mm
• Weight: 424 g
• Illustrations: X, 259 p.
• Series: Lecture Notes in Mathematics; Lecture Notes in Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Arithmetic, algebra; B, Algebraische Topologie, Mathematics and Statistics, Algebraic Geometry, Algebraic Topology, K-Theory