Lectures on algebraic cycles / Spencer Bloch.

Format:

Book

Author/Creator:

Bloch, Spencer, author.

Series:

New mathematical monographs ; 16.

New mathematical monographs ; 16

Language:

English

Subjects (All):

Algebraic cycles.

Physical Description:

1 online resource (xxiv, 130 pages) : digital, PDF file(s).

Edition:

Second edition.

Place of Publication:

Cambridge : Cambridge University Press, 2010.

Language Note:

English

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.

Contents:

Cover; Half-title; Series-title; Title; Copyright; Contents; Preface to the second edition; LECTURES ON ALGEBRAIC CYCLES; 0 Introduction; 1 Zero-cycles on surfaces; 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; Bibliography; Index

Notes:

Title from publisher's bibliographic system (viewed on 05 Oct 2015).

Includes bibliographical references and index.

ISBN:

1-107-20338-4

0-511-76069-8

1-282-74918-8

9786612749186

0-511-90110-0

0-511-90189-5

0-511-79874-1

0-511-79734-6

0-511-90031-7

OCLC:

659500258