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Springer Monographs in Mathematics

Algebraic Cobordism

Authors: Levine, Marc, Morel, Fabien

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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.

Table of contents (7 chapters)

Table of contents (7 chapters)
  • Cobordism and oriented cohomology

    Pages 1-15

  • The definition of algebraic cobordism

    Pages 17-49

  • Fundamental properties of algebraic cobordism

    Pages 51-82

  • Algebraic cobordism and the Lazard ring

    Pages 83-140

  • Oriented Borel-Moore homology

    Pages 141-158

Buy this book

eBook $84.99
price for USA in USD
  • ISBN 978-3-540-36824-3
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $119.99
price for USA in USD
  • ISBN 978-3-540-36822-9
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-3-642-07191-1
  • Free shipping for individuals worldwide
  • Immediate ebook access, if available*, with your print order
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Algebraic Cobordism
Authors
Series Title
Springer Monographs in Mathematics
Copyright
2007
Publisher
Springer-Verlag Berlin Heidelberg
Copyright Holder
Springer-Verlag Berlin Heidelberg
eBook ISBN
978-3-540-36824-3
DOI
10.1007/3-540-36824-8
Hardcover ISBN
978-3-540-36822-9
Softcover ISBN
978-3-642-07191-1
Series ISSN
1439-7382
Edition Number
1
Number of Pages
XII, 246
Topics

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