Algebraic Cobordism

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

Table of contents

About this book

Introduction

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.

Keywords

Chern class Chow ring Cobordism Homotopy K-theory Oriented cohomology theory cohomology cohomology theory homology

Authors and affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA
  2. 2.Mathematisches Institut der LMUMünchenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/3-540-36824-8
  • Copyright Information Springer-Verlag Berlin Heidelberg 2007
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-3-540-36822-9
  • Online ISBN 978-3-540-36824-3
  • Series Print ISSN 1439-7382
  • About this book