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Mixed Motives
 
Marc Levine Northeastern University, Boston, MA
Mixed Motives
Hardcover ISBN:  978-0-8218-0785-9
Product Code:  SURV/57
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-3398-8
Product Code:  SURV/57.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0785-9
eBook: ISBN:  978-0-8218-3398-8
Product Code:  SURV/57.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
Mixed Motives
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Mixed Motives
Marc Levine Northeastern University, Boston, MA
Hardcover ISBN:  978-0-8218-0785-9
Product Code:  SURV/57
List Price: $129.00
MAA Member Price: $116.10
AMS Member Price: $103.20
eBook ISBN:  978-0-8218-3398-8
Product Code:  SURV/57.E
List Price: $125.00
MAA Member Price: $112.50
AMS Member Price: $100.00
Hardcover ISBN:  978-0-8218-0785-9
eBook ISBN:  978-0-8218-3398-8
Product Code:  SURV/57.B
List Price: $254.00 $191.50
MAA Member Price: $228.60 $172.35
AMS Member Price: $203.20 $153.20
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 571998; 515 pp
    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.

    Readership

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

  • Table of Contents
     
     
    • 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
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 571998; 515 pp
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.

Readership

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
Review Copy – for publishers of book reviews
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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