Lectures on Algebraic Cycles

by Spencer Bloch

• ISBN13: 9780521118422
• ISBN10: 0521118425
• Edition: 2nd
• Format: Hardcover
• Copyright: 2010-09-20
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

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.