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.
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