Algebraic geometry is a central subfield of mathematics in which
the study of cycles is an important theme. Alexander Grothendieck
taught that algebraic cycles should be considered from a motivic
point of view and in recent years this topic has spurred a lot of
activity. This book is one of two volumes that provide a
self-contained account of the subject as it stands. Together, the
two books contain twenty-two contributions from leading figures in
the field which survey the key research strands and present
interesting new results. Topics discussed include: the study of
algebraic cycles using Abel-Jacobi/regulator maps and normal
functions; motives (Voevodsky's triangulated category of mixed
motives, finite-dimensional motives); the conjectures of
Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's
conjecture. Researchers and students in complex algebraic geometry
and arithmetic geometry will find much of interest here.
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