Mixed Motives

Know about the book -

Mixed Motives is written by Marc Levine and published by American Mathematical Society. It's available with International Standard Book Number or ISBN identification 1470480190 (ISBN 10) and 9781470480196 (ISBN 13).

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.