Algebraic Cycles and Motives: Volume 1

This 2007 book is a self-contained account of the subject of algebraic cycles and motives.

Jan Nagel (Edited by), Chris Peters (Edited by)

9780521701747, Cambridge University Press

Paperback, published 3 May 2007

308 pages, 8 b/w illus.
22.9 x 15.2 x 1.8 cm, 0.514 kg

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.

Foreword
Part I. Survey Articles: 1. The motivic vanishing cycles and the conservation conjecture J. Ayoub
2. On the theory of 1-motives L. Barbieri-Viale
3. Motivic decomposition for resolutions of threefolds M. de Cataldo and L. Migliorini
4. Correspondences and transfers F. D´eglise
5. Algebraic cycles and singularities of normal functions M. Green and Ph. Griffiths
6. Zero cycles on singular varieties A. Krishna and V. Srinivas
7. Modular curves, modular surfaces and modular fourfolds D. Ramakrishnan.

Subject Areas: Applied mathematics [PBW], Topology [PBP], Geometry [PBM]