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.
Spencer Bloch is R. M. Hutchins Distinguished Service Professor in the Department of Mathematics at the University of Chicago.
Preface to the second edition; Introduction; 1. 0-cycles on surfaces; Lecture 1. Appendix. On an argument of Mumford in the theory of algebraic cycles; 2. Curves on threefolds and intermediate Jacobians; 3. Curves on threefolds and intermediate Jacobians - the relative case; 4. K-theoretic and cohomological methods; 5. Torsion in the Chow group; 6. Complements on H2(K2); 7. Diophantine questions; 8. Relative cycles and zeta functions; 9. Relative cycles and zeta functions (continued); References; Index.