This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for

The primary aim of this monograph is to achieve part of Beilinson’s program on mixed motives using Voevodsky’s theories of A1-homotopy and motivic complexes

The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of i

The conjectural theory of mixed motives would be a universal cohomology theory in arithmetic algebraic geometry. The monograph describes the approach to motives

'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play t