Algebraic Cycles and Motives

by Edited by Jan Nagel , Chris Peters

• ISBN13: 9780521701754
• ISBN10: 0521701759
• Format: Paperback
• Copyright: 2007-05-28
• Publisher: Cambridge University Press

Summary

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 book is one of two volumes that provide a self-contained account of the subject as it stands today. 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.

Table of Contents

Preface	p. ix
Research Articles	p. 1
Beilinson's Hodge Conjecture with Coefficients	p. 3
On the Splitting of the Bloch-Beilinson Filtration	p. 38
Kunneth Projectors	p. 54
The Brill-Noether Curve of a Stable Bundle on a Genus Two Curve	p. 73
On Tannaka Duality for Vector Bundles on p-adic Curves	p. 94
On Finite-dimensional Motives and Murre's Conjecture	p. 112
On the Transcendental Part of the Motive of a Surface	p. 143
A Note on Finite Dimensional Motives	p. 203
Real Regulators on Milnor Complexes, II	p. 214
Motives for Picard Modular Surfaces	p. 241
The Regulator Map for Complete Intersections	p. 277
Hodge Number Polynomials for Nearby and Vanishing Cohomology	p. 289
Direct Image of Logarithmic Complexes	p. 304
Mordell-Weil Lattices of Certain Elliptic K3's	p. 319
Motives from Diffraction	p. 340
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