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This book is an outgrowth of the Workshop on "Regulators in Analysis, Geom etry and Number Theory" held at the Edmund Landau Center for Research in Mathematical Analysis of The Hebrew University of Jerusalem in 1996. During the preparation and the holding of the workshop we were greatly helped by the director of the Landau Center: Lior Tsafriri during the time of the planning of the conference, and Hershel Farkas during the meeting itself. Organizing and running this workshop was a true pleasure, thanks to the expert technical help provided by the Landau Center in general, and by its secretary Simcha Kojman in particular. We would like to express our hearty thanks to all of them. However, the articles assembled in the present volume do not represent the proceedings of this workshop; neither could all contributors to the book make it to the meeting, nor do the contributions herein necessarily reflect talks given in Jerusalem. In the introduction, we outline our view of the theory to which this volume intends to contribute. The crucial objective of the present volume is to bring together concepts, methods, and results from analysis, differential as well as algebraic geometry, and number theory in order to work towards a deeper and more comprehensive understanding of regulators and secondary invariants. Our thanks go to all the participants of the workshop and authors of this volume. May the readers of this book enjoy and profit from the combination of mathematical ideas here documented.
List of contents
Cohomology of Congruence Subgroups of SU(2, 1)P and Hodge Cycles on Some Special Complex Hyperbolic Surfaces.- Remarks on Elliptic Motives.- On Dynamical Systems and Their Possible Significance for Arithmetic Geometry.- Algebraic Differential Characters.- Some Computations in Weight 4 Motivic Complexes.- Geometry of the Trilogarithm and the Motivic Lie Algebra of a Field.- Complex Analytic Torsion Forms for Torus Fibrations and Moduli Spaces.- Théorèmes de Lefschetz et de Hodge arithmétiques pour les variétés admettant une décomposition cellulaire.- Polylogarithmic Currents on Abelian Varieties.- Secondary Analytic Indices.- Variations of Hodge-de Rham Structure and Elliptic Modular Units.
