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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, pushforward for proper maps, RiemannRoch, duality, as well as an associated motivic homology, BorelMoore homology and cohomology with compact supports.
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