Algebraic Cycles and Motives: Volume 1

by Jan Nagel, Chris Peters

Overview

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.

Product Details

ISBN-13:	9780521701747
Publisher:	Cambridge University Press
Publication date:	05/03/2007
Series:	London Mathematical Society Lecture Note Series , #343
Pages:	308
Product dimensions:	5.98(w) x 9.02(h) x 0.71(d)

About the Author

Jan Nagel is a Lecturer at UFR de Mathématiques Pures et Appliquées, Université Lille 1.

Chris Peters is a Professor at Institut Fourier, Université Grenoble 1.

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.