Mixed Motives (Mathematical Surveys and Monographs)

Mixed Motives (Mathematical Surveys and Monographs)


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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.


Motives: 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 Equidimensional 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.

Product Details

  • ISBN13: 9780821807859
  • Format: Hardback
  • ID: 9780821807859
  • ISBN10: 0821807854

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