The Arithmetic and Geometry of Algebraic Cycles (CRM Proceedings & Lecture Notes): Proceedings of the Crm Summer School, June 7-19, 1998, Banff, Alberta, Canada - Softcover

American Mathematical Society

Softcover

ISBN 10: 0821819542 ISBN 13: 9780821819548

Publisher: American Mathematical Society, 2000

Synopsis

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 etale cohomology; and, 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.

Edition details

• Publisher: American Mathematical Society
• Publication date: 2000
• Language: English
• ISBN 10: 0821819542
• ISBN 13: 9780821819548
• Binding: Paperback
• Number of pages: 432