Lectures on Algebraic Cycles
“Lectures on Algebraic Cycles” by Spencer Bloch is a significant work published by Cambridge University Press on July 22, 2010. This 156-page edition presents Bloch’s influential 1979 Duke lectures, which have been a key resource for understanding the philosophy of algebraic cycles and motives since their initial release in 1980. The book is now professionally typeset and includes a new preface by the author, reflecting on developments in the field over the past three decades.
Readers will find a comprehensive exploration of central problems in mathematics, including the Hodge conjecture and the Bloch-Kato conjecture related to special values of zeta functions. The text begins with an example from Mumford, illustrating the infinite-dimensional nature of the Chow group of zero-cycles on an algebraic variety. It further delves into how Hodge theory and algebraic K-theory provide new insights into these phenomena, making it a valuable resource for those interested in mathematics, topology, geometry, and number theory.
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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.
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