Skip to main content
SpringerLink
Log in
Book cover

A1-Algebraic Topology over a Field

  • Book
  • © 2012

Overview

Authors:
  1. Fabien Morel

    1. Institut für Mathematik, Universität München, München, Germany

    View author publications

    You can also search for this author in PubMed   Google Scholar

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

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 49.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 64.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (9 chapters)

  1. Front Matter

    Pages i-x
    Download chapter PDF

  2. Introduction

    • Fabien Morel
    Pages 1-13

  3. Unramified Sheaves and Strongly \({\mathbb{A}}^{1}\)-Invariant Sheaves

    • Fabien Morel
    Pages 15-48

  4. Unramified Milnor–Witt K-Theories

    • Fabien Morel
    Pages 49-80

  5. Geometric Versus Canonical Transfers

    • Fabien Morel
    Pages 81-112

  6. The Rost–Schmid Complex of a Strongly \({\mathbb{A}}^{1}\)-Invariant Sheaf

    • Fabien Morel
    Pages 113-148

  7. \({\mathbb{A}}^{1}\)-Homotopy Sheaves and \({\mathbb{A}}^{1}\)-Homology Sheaves

    • Fabien Morel
    Pages 149-175

  8. \({\mathbb{A}}^{1}\)-Coverings, \({\pi }_{1}^{{\mathbb{A}}^{1} }({\mathbb{P}}^{n})\) and \({\pi }_{1}^{{\mathbb{A}}^{1} }(S{L}_{n})\)

    • Fabien Morel
    Pages 177-197

  9. \({\mathbb{A}}^{1}\)-Homotopy and Algebraic Vector Bundles

    • Fabien Morel
    Pages 199-207

  10. The Affine B.G. Property for the Linear Groups and the Grassmanian

    • Fabien Morel
    Pages 209-226

  11. Back Matter

    Pages 227-259
    Download chapter PDF
Back to top

Keywords

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.

Authors and Affiliations

  • Institut für Mathematik, Universität München, München, Germany

    Fabien Morel

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation