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Lectures on Algebraic Cycles : New Mathematical Monographs - Spencer J. Bloch

Lectures on Algebraic Cycles

New Mathematical Monographs

Hardcover

Published: 22nd July 2010
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Spencer Bloch's 1979 Duke lectures, a milestone in modern mathematics, have been out of print almost since their first publication in 1980, yet they have remained influential and are still the best place to learn the guiding philosophy of algebraic cycles and motives. This edition, now professionally typeset, has a new preface by the author giving his perspective on developments in the field over the past 30 years. The theory of algebraic cycles encompasses such central problems in mathematics as the Hodge conjecture and the Bloch-Kato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zero-cycles on an algebraic variety can be infinite-dimensional, and explains how Hodge theory and algebraic K-theory give new insights into this and other phenomena.

Preface to the second edition
Introduction
0-cycles on surfaces
Appendix. On an argument of Mumford in the theory of algebraic cycles
Curves on threefolds and intermediate Jacobians
Curves on threefolds and intermediate Jacobians - the relative case
K-theoretic and cohomological methods
Torsion in the Chow group
Complements on H2(K2)
Diophantine questions
Relative cycles and zeta functions
Relative cycles and zeta functions (continued)
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521118422
ISBN-10: 0521118425
Series: New Mathematical Monographs
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 156
Published: 22nd July 2010
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 1.5
Weight (kg): 0.4
Edition Number: 2
Edition Type: Revised