**CRM Proceedings & Lecture Notes**

Volume: 24;
2000;
432 pp;
Softcover

MSC: Primary 11; 14; 19;
**Print ISBN: 978-0-8218-1954-8
Product Code: CRMP/24**

List Price: $128.00

Individual Member Price: $102.40

# The Arithmetic and Geometry of Algebraic Cycles

Share this page *Edited by *
*B. Brent Gordon; James D. Lewis; Stefan Müller-Stach; Shuji Saito; Noriko Yui*

A co-publication of the AMS and Centre de Recherches Mathématiques

The NATO ASI/CRM Summer School at Banff offered a unique, full, and in-depth 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 Merkurjev-Suslin theorem to the arithmetic Abel-Jacobi 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 non-zero 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 co-published with the Centre de Recherches Mathématiques.

#### Table of Contents

# Table of Contents

## The Arithmetic and Geometry of Algebraic Cycles

#### Readership

Graduate students and research mathematicians interested in algebraic cycles.