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Algebraic Cobordism
Springer Monographs in Mathematics
ISBN/EAN: 9783540368229
Umbreit-Nr.: 1171710
Sprache:
Englisch
Umfang: xii, 246 S.
Format in cm:
Einband:
gebundenes Buch
Erschienen am 09.01.2007
Auflage: 1/2007
- Zusatztext
- InhaltsangabeCobordism and oriented cohomology.- The definition of algebraic cobordism.- Fundamental properties of algebraic cobordism.- Algebraic cobordism and the Lazard ring.- Oriented Borel-Moore homology.- Functoriality.- The universality of algebraic cobordism.
- Kurztext
- 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.