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Algebraic Cobordism

Algebraic Cobordism by Marc Levine
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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 positive degrees. This implies in particular the generalized degree formula conjectured by Rost. The book also contains some examples of computations and applications.
Springer Berlin Heidelberg; February 2007
254 pages; ISBN 9783540368243
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Title: Algebraic Cobordism
Author: Marc Levine; Fabien Morel
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