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Mixed Motives
Marc Levine, Northeastern University, Boston, MA

Mathematical Surveys and Monographs
1998; 515 pp; hardcover
Volume: 57
ISBN-10: 0-8218-0785-4
ISBN-13: 978-0-8218-0785-9
List Price: US$132
Member Price: US$105.60
Order Code: SURV/57
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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.


"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

  • Introduction: Part I
  • The motivic category
  • Motivic cohomology and higher Chow groups
  • K-theory and motives
  • Homology, cohomology and duality
  • Realization of the motivic category
  • Motivic constructions and comparisons
  • Equi-dimensional cycles
  • K-theory
Categorical algebra
  • Introduction: Part II
  • Symmetric monoidal structures
  • DG categories and triangulated categories
  • Simplicial and cosimplicial constructions
  • Canonical models for cohomology
  • Bibliography
  • Subject index
  • Index of notation
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