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＜電子ブック＞
Algebraic Cobordism / by Marc Levine, Fabien Morel
(Springer Monographs in Mathematics. ISSN:21969922)

版	1st ed. 2007.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2007
本文言語	英語
大きさ	XII, 246 p : online resource
著者標目	*Levine, Marc author Morel, Fabien author SpringerLink (Online service)
件　名	LCSH:Algebraic topology LCSH:Topology LCSH:Algebraic geometry LCSH:Commutative algebra LCSH:Commutative rings LCSH:K-theory FREE:Algebraic Topology FREE:Topology FREE:Algebraic Geometry FREE:Commutative Rings and Algebras FREE:K-Theory
一般注記	Introduction -- I. Cobordism and oriented cohomology -- 1.1. Oriented cohomology theories. 1.2. Algebraic cobordism. 1.3. Relations with complex cobordism. - II. The definition of algebraic cobordism. 2.1. Oriented Borel-Moore functions. 2.2. Oriented functors of geometric type. 2.3. Some elementary properties. 2.4. The construction of algebraic cobordism. 2.5. Some computations in algebraic cobordism -- III. Fundamental properties of algebraic cobordism. 3.1. Divisor classes. 3.2. Localization. 3.3. Transversality. 3.4. Homotopy invariance. 3.5. The projective bundle formula. 3.6. The extended homotopy property. IV. Algebraic cobordism and the Lazard ring. 4.1. Weak homology and Chern classes. 4.2. Algebraic cobordism and K-theory. 4.3. The cobordism ring of a point. 4.4. Degree formulas. 4.5. Comparison with the Chow groups. V. Oriented Borel-Moore homology. 5.1. Oriented Borel-Moore homology theories. 5.2. Other oriented theories -- VI. Functoriality. 6.1. Refined cobordism. 6.2. Intersection with a pseudo-divisor. 6.3. Intersection with a pseudo-divisor II. 6.4. A moving lemma. 6.5. Pull-back for l.c.i. morphisms. 6.6. Refined pull-back and refined intersections. VII. The universality of algebraic cobordism. 7.1. Statement of results. 7.2. Pull-back in Borel-Moore homology theories. 7.3. Universality 7.4. Some applications -- Appendix A: Resolution of singularities -- References -- Index -- Glossary of Notation 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 HTTP:URL=https://doi.org/10.1007/3-540-36824-8

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