Algebraic Cycles and Motives: Volume 1
Title | Algebraic Cycles and Motives: Volume 1 PDF eBook |
Author | Jan Nagel |
Publisher | Cambridge University Press |
Total Pages | 293 |
Release | 2007-05-03 |
Genre | Mathematics |
ISBN | 0521701740 |
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Motives
Title | Motives PDF eBook |
Author | |
Publisher | American Mathematical Soc. |
Total Pages | 694 |
Release | 1994-02-28 |
Genre | Mathematics |
ISBN | 0821827987 |
'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
Title | Lectures on Algebraic Cycles PDF eBook |
Author | Spencer Bloch |
Publisher | Cambridge University Press |
Total Pages | 155 |
Release | 2010-07-22 |
Genre | Mathematics |
ISBN | 1139487825 |
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.
Mixed Motives and Algebraic K-Theory
Title | Mixed Motives and Algebraic K-Theory PDF eBook |
Author | Uwe Jannsen |
Publisher | Springer |
Total Pages | 260 |
Release | 2006-11-14 |
Genre | Mathematics |
ISBN | 3540469419 |
The relations that could or should exist between algebraic cycles, algebraic K-theory, and the cohomology of - possibly singular - varieties, are the topic of investigation of this book. The author proceeds in an axiomatic way, combining the concepts of twisted Poincaré duality theories, weights, and tensor categories. One thus arrives at generalizations to arbitrary varieties of the Hodge and Tate conjectures to explicit conjectures on l-adic Chern characters for global fields and to certain counterexamples for more general fields. It is to be hoped that these relations ions will in due course be explained by a suitable tensor category of mixed motives. An approximation to this is constructed in the setting of absolute Hodge cycles, by extending this theory to arbitrary varieties. The book can serve both as a guide for the researcher, and as an introduction to these ideas for the non-expert, provided (s)he knows or is willing to learn about K-theory and the standard cohomology theories of algebraic varieties.
Algebraic Cycles and Motives: Volume 2
Title | Algebraic Cycles and Motives: Volume 2 PDF eBook |
Author | Jan Nagel |
Publisher | Cambridge University Press |
Total Pages | 360 |
Release | 2007-05-03 |
Genre | Mathematics |
ISBN | 0521701759 |
A self-contained account of the subject of algebraic cycles and motives as it stands.
Group Cohomology and Algebraic Cycles
Title | Group Cohomology and Algebraic Cycles PDF eBook |
Author | Burt Totaro |
Publisher | Cambridge University Press |
Total Pages | 245 |
Release | 2014-06-26 |
Genre | Mathematics |
ISBN | 1107015774 |
This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Cycles, Transfers, and Motivic Homology Theories. (AM-143)
Title | Cycles, Transfers, and Motivic Homology Theories. (AM-143) PDF eBook |
Author | Vladimir Voevodsky |
Publisher | Princeton University Press |
Total Pages | 262 |
Release | 2000 |
Genre | Mathematics |
ISBN | 0691048150 |
The original goal that ultimately led to this volume was the construction of "motivic cohomology theory," whose existence was conjectured by A. Beilinson and S. Lichtenbaum. This is achieved in the book's fourth paper, using results of the other papers whose additional role is to contribute to our understanding of various properties of algebraic cycles. The material presented provides the foundations for the recent proof of the celebrated "Milnor Conjecture" by Vladimir Voevodsky. The theory of sheaves of relative cycles is developed in the first paper of this volume. The theory of presheaves with transfers and more specifically homotopy invariant presheaves with transfers is the main theme of the second paper. The Friedlander-Lawson moving lemma for families of algebraic cycles appears in the third paper in which a bivariant theory called bivariant cycle cohomology is constructed. The fifth and last paper in the volume gives a proof of the fact that bivariant cycle cohomology groups are canonically isomorphic (in appropriate cases) to Bloch's higher Chow groups, thereby providing a link between the authors' theory and Bloch's original approach to motivic (co-)homology.