Lecture Notes in Mathematics

A1-Algebraic Topology over a Field

Authors: Morel, Fabien

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About this book

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 (9 chapters)

  • Introduction

    Morel, Fabien

    Pages 1-13

  • Unramified Sheaves and Strongly $${\mathbb{A}}^{1}$$ -Invariant Sheaves

    Morel, Fabien

    Pages 15-48

  • Unramified Milnor–Witt K-Theories

    Morel, Fabien

    Pages 49-80

  • Geometric Versus Canonical Transfers

    Morel, Fabien

    Pages 81-112

  • The Rost–Schmid Complex of a Strongly $${\mathbb{A}}^{1}$$ -Invariant Sheaf

    Morel, Fabien

    Pages 113-148

Buy this book

eBook $44.99
price for USA (gross)
  • ISBN 978-3-642-29514-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $59.95
price for USA
  • ISBN 978-3-642-29513-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the ebook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
A1-Algebraic Topology over a Field
Authors
Series Title
Lecture Notes in Mathematics
Series Volume
2052
Copyright
2012
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-642-29514-0
DOI
10.1007/978-3-642-29514-0
Softcover ISBN
978-3-642-29513-3
Series ISSN
0075-8434
Edition Number
1
Number of Pages
X, 259
Topics