Algebraic cycles and motives. Volume 1 /
Algebraic Cycles & Motives
edited by Jan Nagel, Chris Peters.
- Cambridge : Cambridge University Press, 2007.
- 1 online resource (xiv, 292 pages) : digital, PDF file(s).
- London Mathematical Society lecture note series ; 343 .
- London Mathematical Society lecture note series ; 343. .
Title from publisher's bibliographic system (viewed on 05 Oct 2015).
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.