Algebraic Cobordism

• Main Authors: Levine, Marc (Author), Morel, Fabien (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2007.
• Series: Springer Monographs in Mathematics,
• Subjects: Mathematics.; Algebraic geometry.; Commutative algebra.; Commutative rings.; K-theory.; Topology.; Algebraic topology.; Algebraic Topology.; Algebraic Geometry.; Commutative Rings and Algebras.; K-Theory.
• Physical Description: XII, 246 p. online resource.
• ISBN: 9783540368243
• ISSN: 1439-7382

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.