CRM Proceedings & Lecture Notes 2000; 432 pp; softcover Volume: 24 ISBN10: 0821819542 ISBN13: 9780821819548 List Price: US$128 Member Price: US$102.40 Order Code: CRMP/24
 The NATO ASI/CRM Summer School at Banff offered a unique, full, and indepth account of the topic, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods. As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic \(K\)theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to developments such as a description of Chow groups in terms of algebraic \(K\)theory, the application of the MerkurjevSuslin theorem to the arithmetic AbelJacobi mapping, progress on the celebrated conjectures of Hodge, and of Tate, which compute cycles class groups respectively in terms of Hodge theory or as the invariants of a Galois group action on étale cohomology, the conjectures of Bloch and Beilinson, which explain the zero or pole of the \(L\)function of a variety and interpret the leading nonzero coefficient of its Taylor expansion at a critical point, in terms of arithmetic and geometric invariant of the variety and its cycle class groups. The immense recent progress in the theory of algebraic cycles is based on its many interactions with several other areas of mathematics. This conference was the first to focus on both arithmetic and geometric aspects of algebraic cycles. It brought together leading experts to speak from their various points of view. A unique opportunity was created to explore and view the depth and the breadth of the subject. This volume presents the intriguing results. Titles in this series are copublished with the Centre de Recherches Mathématiques. Readership Graduate students and research mathematicians interested in algebraic cycles. Table of Contents Cohomological Methods  S. Abdulali  Filtrations on the cohomology of abelian varieties
 D. Arapura  Building mixed Hodge structures
 R.O. Buchweitz and H. Flenner  The AtiyahChern character yields the semiregularity map as well as the infinitesimal AbelJacobi map
 J. Dupont, R. Hain, and S. Zucker  Regulators and characteristic classes of flat bundles
 B. Harris and B. Wang  Height pairings asymptotics and BottChern forms
 K. Kato and S. Usui  Logarithmic Hodge structures and classifying spaces
Chow Groups and Motives  M. Asakura  Motives and algebraic de Rham cohomology
 J. I. Burgos Gil  Hermitian vector bundles and characteristic classes
 M. Hanamura  The mixed motive of a projective variety
 C. Pedrini  Bloch's conjecture and the \(K\)theory of projective surfaces
 N. Ramachandran  From Jacobians to onemotives: Exposition of a conjecture of Deligne
 S. Saito  Motives, algebraic cycles and Hodge theory
Arithmetic methods  C. F. Doran  PicardFuchs uniformization: Modularity of the mirror map and mirrormoonshine
 E. Z. Goren  Hilbert modular varieties in positive characteristic
 Y. Goto  On the NéronSeveri groups of some \(K\)3 surfaces
 J. van Hamel  Torsion zerocycles and the AbelJacobi map over the real numbers
 K. Kimura  A remark on the Griffiths groups of certain product varieties
 J. Nekovář  \(p\)adic AbelJacobi maps and \(p\)adic heights
 A. Shiho  Crystalline fundamental groups and \(p\)adic Hodge theory
 H. Verrill and N. Yui  Thompson series, and the mirror maps of pencils of \(K\)3 surfaces
