Algebraic Cycles and Motives: Volume 2

Jan Nagel, Chris Peters

• Publisher: Cambridge University Press
• Year: 2007
• Print ISBN: 9780521701754
• eBook ISBN: 9781107109209
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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. 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

• Cover
• Series Page
• Title
• Copyright
• Contents of Volume 2
• Contents of Volume 1
• Preface
• Volume 2: Research Articles
• 1 Beilinson’s Hodge Conjecture with Coefficients for Open Complete Intersections
• 2 On the Splitting of the Bloch-Beilinson Filtration
• 3 Künneth Projectors for Open Varieties
• 4 The Brill-Noether Curve of a stable Vector Bundle on a Genus Two Curve
• 5 On Tannaka duality for vector bundles on p-adic curves
• 6 On finite-dimensional motives and Murre’s conjecture
• 7 On the Transcendental Part of the Motive of a Surface
• 8 A note on finite dimensional motives
• 9 Real Regulators on Milnor Complexes, II
• 10 Chow-K¨unneth decomposition for universal families over Picard modular surfaces
• 11 The Regulator Map for Complete Intersections
• 12 Hodge Number Polynomials for Nearby and Vanishing Cohomology
• 13 Direct Image of Logarithmic Complexes and Infinitesimal Invariants of Cycles
• 14 Correspondence of Elliptic Curves and Mordell-Weil Lattices of Certain Elliptic K3’s
• 15 Motives from Diffraction