A[1]-algebraic topology over a field

Author(s)

• Morel, Fabien

Bibliographic Information

A[1]-algebraic topology over a field

Fabien Morel

（Lecture notes in mathematics, 2052）

Springer, c2012

Note

[1] is superscript

Includes bibliographical references (p. 255-258) and index

Description and Table of Contents

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

Table 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

by "Nielsen BookData"

Details

• NCID: BB0991870X
• ISBN:
  • 9783642295133
• LCCN: 2012942079
• Country Code: gw
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Heidelberg
• Pages/Volumes: x, 259 p.
• Size: 24 cm
• Classification:
  • DC23 : 514.24
• Subject Headings:
  • LCSH : Homotopy theory
  • LCSH : Algebraic topology
• Parent Bibliography ID:
  • BA00146586