Motives

Motives PDF

Author:

Publisher: American Mathematical Soc.

Published: 1994-02-28

Total Pages: 694

ISBN-13: 0821827987

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'Motives' were introduced in the mid-1960s by Grothendieck to explain the analogies among the various cohomology theories for algebraic varieties, and to play the role of the missing rational cohomology. This work contains the texts of the lectures presented at the AMS-IMS-SIAM Joint Summer Research Conference on Motives, held in Seattle, in 1991.

Lectures on Algebraic Cycles

Lectures on Algebraic Cycles PDF

Author: Spencer Bloch

Publisher: Cambridge University Press

Published: 2010-07-22

Total Pages: 155

ISBN-13: 1139487825

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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.

Group Cohomology and Algebraic Cycles

Group Cohomology and Algebraic Cycles PDF

Author: Burt Totaro

Publisher: Cambridge University Press

Published: 2014-06-26

Total Pages: 245

ISBN-13: 1107015774

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This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.

The Geometry of Algebraic Cycles

The Geometry of Algebraic Cycles PDF

Author: Reza Akhtar

Publisher: American Mathematical Soc.

Published: 2010

Total Pages: 202

ISBN-13: 0821851918

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The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.