Algebraic Cycles and Motives
Algebraic Cycles and Motives
£67.99
GBPAlgebraic 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.
- Provides a self-contained account of the subject of algebraic cycles and motives
- Papers by the leading experts in the field
- Discusses both main research topics and interesting developments within the subject
Product details
May 2007Paperback
9780521701747
308 pages
229 × 152 × 18 mm
0.514kg
8 b/w illus.
Available
Table of Contents
- 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.
