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Algebraic cobordism

Author: Marc Levine; Fabien Morel
Publisher: Berlin : Springer, ©2007.
Series: Springer monographs in mathematics.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Database:WorldCat
Summary:
"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. The book also contains some examples of computations and applications."--Jacket.
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Levine, Marc, 1952-
Algebraic cobordism.
Berlin : Springer, ©2007
(DLC) 2006936486
(OCoLC)85804043
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Marc Levine; Fabien Morel
ISBN: 9783540368243 3540368248 3540368221 9783540368229
OCLC Number: 185022118
Description: 1 online resource (xii, 244 pages) : illustrations.
Contents: 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.
Series Title: Springer monographs in mathematics.
Responsibility: M. Levine, F. Morel.

Abstract:

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  Read more...

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