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# ðŸ“™ The arithmetic and geometry of algebraic cycles: proceedings of the CRM summer school, June 7-19, 1998, Banff, Alberta, Canada by B. Brent Gordon, James D. Lewis, Stefan MÃ¼ller-Stach, Shuji Saito, Noriko Yui (editors) â€” pdf free

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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 Ã©tale 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 MathÃ©matiques.

## About book:

## About file:

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- Series:
**CRM proceedings & lecture notes #24** - Author:
**B. Brent Gordon, James D. Lewis, Stefan MÃ¼ller-Stach, Shuji Saito, Noriko Yui (editors)** - Year:
**2000** - Publisher:
**American Mathematical Society** - Language:
**English** - ISBN:
**0821819542,9780821819548**

- DPI:
**600** - File size:
**4 196 765** - Format:
**djvu**

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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 thre...

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 thre...

Topics range from introductory lectures on algebraic cycles to more advanced material in this collection of lecture notes from the Proceedings of the Grenoble Summer School, 2001. The advanced lectures are grouped under three headings: Lawson (co)homology...

The Centre de recherches matMmatiques (CRM) was created in 1968 by the Universite de Montreal to promote research in the mathematical sciences. It is now a national institute that hosts several groups and holds special theme years, summer schools, worksho...

This book resulted from a research conference in arithmetic geometry held at Arizona State University in March 1993. The papers describe important recent advances in arithmetic geometry. Several articles deal with p-adic modular forms of half-integral wei...

For the second time, a Summer School in Analysis and Mathematical Physics took place at the Universidad Nacional Autonoma de Mexico in Cuernavaca. The purpose of the schools is to provide a bridge from standard graduate courses in mathematics to current r...

The Marktoberdorf Summer Schools on Informatics were started in 1970, with the intention to convene every second or third year a group of top researchers in computing, devoted to preach their most recent results to an elite of advanced students - young an...

This volume comprises the Lecture Notes of the CIMPA Summer School "Arithmetic and Geometry around Hypergeometric Functions" held at Galatasaray University, Istanbul in 2005. It contains lecture notes, a survey article, research articles, and the results ...

Arithmetic Geometry can be defined as the part of Algebraic Geometry connected with the study of algebraic varieties over arbitrary rings, in particular over non-algebraically closed fields. It lies at the intersection between classical algebraic geometry...