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A1-Algebraic Topology over a Field

  • Fabien Morel

Part of the Lecture Notes in Mathematics book series (LNM, volume 2052)

About this book

Introduction

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.

Keywords

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

Authors and affiliations

  • Fabien Morel
    • 1
  1. 1.Institut für MathematikUniversität MünchenMünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-29514-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 2012
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-642-29513-3
  • Online ISBN 978-3-642-29514-0
  • Series Print ISSN 0075-8434
  • Series Online ISSN 1617-9692
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