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.

Book Information
ISBN 9783540368229
Author Marc Levine
Format Hardback
Page Count 246
Imprint Springer-Verlag Berlin and Heidelberg GmbH & Co. K
Publisher Springer-Verlag Berlin and Heidelberg GmbH & Co. KG