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Mixed Motives

Marc Levine Northeastern University, Boston, MA
Available Formats:
Hardcover ISBN: 978-0-8218-0785-9
Product Code: SURV/57
515 pp
List Price: $132.00 MAA Member Price:$118.80
AMS Member Price: $105.60 Electronic ISBN: 978-0-8218-3398-8 Product Code: SURV/57.E 515 pp List Price:$132.00
MAA Member Price: $118.80 AMS Member Price:$105.60
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This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $198.00 MAA Member Price:$178.20
AMS Member Price: $158.40 Click above image for expanded view Mixed Motives Marc Levine Northeastern University, Boston, MA Available Formats:  Hardcover ISBN: 978-0-8218-0785-9 Product Code: SURV/57 515 pp  List Price:$132.00 MAA Member Price: $118.80 AMS Member Price:$105.60
 Electronic ISBN: 978-0-8218-3398-8 Product Code: SURV/57.E 515 pp
 List Price: $132.00 MAA Member Price:$118.80 AMS Member Price: $105.60 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$198.00
MAA Member Price: $178.20 AMS Member Price:$158.40
• Book Details

Mathematical Surveys and Monographs
Volume: 571998
MSC: Primary 19; 14;

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.

Graduate students and research mathematicians interested in algebraic geometry and $K$-theory.

• 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
• Reviews

• 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
• Request Review Copy
• Get Permissions
Volume: 571998
MSC: Primary 19; 14;

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.

Graduate students and research mathematicians interested in algebraic geometry and $K$-theory.

• 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
• 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
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