**Mathematical Surveys and Monographs**

Volume: 57;
1998;
515 pp;
Hardcover

MSC: Primary 19; 14;

Print ISBN: 978-0-8218-0785-9

Product Code: SURV/57

List Price: $132.00

Individual Member Price: $105.60

**Electronic ISBN: 978-0-8218-3398-8
Product Code: SURV/57.E**

List Price: $132.00

Individual Member Price: $105.60

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# Mixed Motives

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*Marc Levine*

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.

#### Readership

Graduate students and research mathematicians interested in algebraic geometry and \(K\)-theory.

#### Reviews & Endorsements

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 Society

#### Table of Contents

# Table of Contents

## Mixed Motives

- Contents vii8 free
- Preface ix10 free
- Part I. Motives 112 free
- Introduction: Part I 314
- Chapter I. The Motivic Category 718
- Chapter II. Motivic Cohomology and Higher Chow Groups 5364
- Chapter III. K-Theory and Motives 107118
- Chapter IV. Homology, Cohomology, and Duality 191202
- Chapter V. Realization of the Motivic Category 255266
- Chapter VI. Motivic Constructions and Comparisons 293304
- Appendix A. Equi-dimensional Cycles 331342
- Appendix B. K-Theory 357368

- Part II. Categorical Algebra 371382
- Bibliography 501512
- Subject Index 507518
- Index of Notation 513524 free