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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.
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- Title Algebraic Cobordism
- Author Marc Levine; Fabien Morel
- Binding Hardcover
- Edition U. S. EDITION
- Pages 246
- Volumes 1
- Language ENG
- Publisher Springer, china
- Date 2007-01-09
- Features Bibliography, Index, Table of Contents
- ISBN 9783540368229 / 3540368221
- Weight 1.11 lbs (0.50 kg)
- Dimensions 9.4 x 6.36 x 0.77 in (23.88 x 16.15 x 1.96 cm)
- Library of Congress Catalog Number 2006936486
- Dewey Decimal Code 514.72
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Algebraic Cobordism (Springer Monographs in Mathematics)
by M. Levine/ F. Morel
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Algebraic Cobordism
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Hardback. New. 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. The book also contains some examples of computations and applications.
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