Mathematical Surveys and Monographs 1998; 515 pp; hardcover Volume: 57 ISBN10: 0821807854 ISBN13: 9780821807859 List Price: US$132 Member Price: US$105.60 Order Code: SURV/57
 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, pushforward for proper maps, RiemannRoch, duality, as well as an associated motivic homology, BorelMoore homology and cohomology with compact supports. Readership Graduate students and research mathematicians interested in algebraic geometry and \(K\)theory. 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 Table of Contents Motives  Introduction: Part I
 The motivic category
 Motivic cohomology and higher Chow groups
 Ktheory and motives
 Homology, cohomology and duality
 Realization of the motivic category
 Motivic constructions and comparisons
 Equidimensional cycles
 Ktheory
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
