Algebraic Cycles and Motives: Volume 1

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 2007 book is one of two volumes that provide a self-contained account of the subject.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.