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Algebraic Cobordism

  • Book
  • © 2007

Overview

Authors:
  1. Marc Levine

    1. Department of Mathematics, Northeastern University, Boston, USA

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  2. Fabien Morel

    1. Mathematisches Institut der LMU, München, Germany

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Springer Monographs in Mathematics (SMM)

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-XII
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  2. Cobordism and oriented cohomology

    Pages 1-15

  3. The definition of algebraic cobordism

    Pages 17-49

  4. Fundamental properties of algebraic cobordism

    Pages 51-82

  5. Algebraic cobordism and the Lazard ring

    Pages 83-140

  6. Oriented Borel-Moore homology

    Pages 141-158

  7. Functoriality

    Pages 159-213

  8. The universality of algebraic cobordism

    Pages 215-231

  9. Back Matter

    Pages 233-246
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Keywords

About this book

Following Quillen's approach to complex cobordism, the authors introduce the notion of oriented cohomology theory on the category of smooth varieties over a fixed field. They prove the existence of a universal such theory (in characteristic 0) called Algebraic Cobordism. Surprisingly, this theory satisfies the analogues of Quillen's theorems: the cobordism of the base field is the Lazard ring and the cobordism of a smooth variety is generated over the Lazard ring by the elements of positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications.

Authors and Affiliations

  • Department of Mathematics, Northeastern University, Boston, USA

    Marc Levine

  • Mathematisches Institut der LMU, München, Germany

    Fabien Morel

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