Algebraic Cobordism

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.

Info autore

Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.

Riassunto

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.

Dettagli sul prodotto

• Autori: Mar Levine, Fabien Morel, Marc Levine, F. Morel, M. Levine
• Editore: Springer, Berlin
• Contenuto: Libro
• Forma del prodotto: Copertina rigida
• Data pubblicazione: 04.09.2007
• Categoria: Scienze naturali, medicina, informatica, tecnica > Matematica > Geometria
• EAN: 9783540368229
• ISBN: 978-3-540-36822-9
• Numero di pagine: 246
• Illustrazioni: XII, 246 p.
• Dimensioni (della confezione): 15.5 x 1.7 x 23.5 cm
• Peso (della confezione): 502 g
• Serie: Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing; Springer Monographs in Mathematics; Schriftenreihe Markt und Marketing
• Categorie: Algebra, B, Topologie, Algebraische Geometrie, Mathematics and Statistics, Topology, Algebraic Geometry, Commutative algebra, Commutative rings, Commutative Rings and Algebras, Algebraic Topology, K-Theory