
Mixed Motives
Marc Levine(Author)
American Mathematical Society (Publisher)
Published on 30. December 1998
Book
Paperback/Softback
515 pages
978-1-4704-8019-6 (ISBN)
Description
This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry. The author constructs and describes a triangulated category of mixed motives over an arbitrary base scheme. Most of the classical constructions of cohomology are described in the motivic setting, including Chern classes from higher $K$-theory, push-forward for proper maps, Riemann-Roch, duality, as well as an associated motivic homology, Borel-Moore homology and cohomology with compact supports.
Reviews / Votes
All in all, everyone interested in mixed motives and willing to take a serious look at the topic, should try his/her hand on this impressive work. - Zentralblatt MATH We must go out of our way to ensure that our libraries acquire books like this, and then we should 'encourage' our best PhD students to read them! ""- Bulletin of the London Mathematical SocietyMore details
Series
Language
English
Place of publication
Providence
United States
Target group
Professional and scholarly
ISBN-13
978-1-4704-8019-6 (9781470480196)
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Schweitzer Classification
Person
Marc Levine, Northeastern University, Boston, MA
Content
Part I. Motives
I. The motivic category
II. Motivic cohomology and higher Chow groups
III. K-theory and motives
IV. Homology, cohomology, and duality
V. Realization of the motivic category
VI. Motivic constructions and comparisons
Appendix A. Equi-dimensional cycles
Appendix B. K-theory
Part II. Categorical algebra
I. Symmetric monoidal structures
II. DG categories and triangulated categories
III. Simplicial and cosimplicial constructions
IV. Canonical models for cohomology
I. The motivic category
II. Motivic cohomology and higher Chow groups
III. K-theory and motives
IV. Homology, cohomology, and duality
V. Realization of the motivic category
VI. Motivic constructions and comparisons
Appendix A. Equi-dimensional cycles
Appendix B. K-theory
Part II. Categorical algebra
I. Symmetric monoidal structures
II. DG categories and triangulated categories
III. Simplicial and cosimplicial constructions
IV. Canonical models for cohomology