Algebraic Cobordism |
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| Author:
| Levine, Marc
Morel, Fabien |
| Series title: | Springer Monographs in Mathematics Ser. |
| ISBN: | 978-3-540-36824-3 |
| Publication Date: | Feb 2007 |
| Publisher: | Springer London, Limited
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| Book Format: | Ebook |
| List Price: | USD $119.00 |
Book Description:
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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...
More DescriptionFollowing 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.