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Lectures on Algebraic Cycles (New Mathematical Monographs, Series Number 16),New
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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 BlochKato conjecture on special values of zeta functions. The book begins with Mumford's example showing that the Chow group of zerocycles on an algebraic variety can be infinitedimensional, and explains how Hodge theory and algebraic Ktheory give new insights into this and other phenomena.
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