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| 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.
| Author | : Rob de Jeu |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 354 |
| Release | : 2009 |
| Genre | : Mathematics |
| ISBN | : 0821844946 |
Spencer J. Bloch has, and continues to have, a profound influence on the subject of Algebraic $K$-Theory, Cycles and Motives. This book, which is comprised of a number of independent research articles written by leading experts in the field, is dedicated in his honour, and gives a snapshot of the current and evolving nature of the subject. Some of the articles are written in an expository style, providing a perspective on the current state of the subject to those wishing to learn more about it. Others are more technical, representing new developments and making them especially interesting to researchers for keeping abreast of recent progress.
| 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.
| 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.
| 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.
| 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.
| 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.
| Author | : B. Brent Gordon |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 631 |
| Release | : 2012-12-06 |
| Genre | : Mathematics |
| ISBN | : 9401140987 |
The NATO Advanced Study Institute on "The Arithmetic and Geometry of Algebraic Cycles" was held at the Banff Centre for Conferences in Banff (Al berta, Canada) from June 7 until June 19, 1998. This meeting was organized jointly with Centre de Recherches Mathematiques (CRM), Montreal, as one of the CRM Summer schools which take place annually at the Banff Center. The conference also served as the kick-off activity of the CRM 1998-99 theme year on Number Theory and Arithmetic Geometry. There were 109 participants who came from 17 countries: Belgium, Canada, China, France, Germany, Greece, India, Italy, Japan, Mexico, Netherlands, - mania, Russia, Spain, Switzerland, the United Kingdom and the United States. During a period of two weeks, 41 invited lectures and 20 contributed lec tures were presented. Four lectures by invited speakers were delivered every day, followed by two sessions of contributed talks. Many informal discussions and working sessions involving small groups were organized by individual partic ipants. In addition, participants' reprints and preprints were displayed through out in a lounge next to the auditorium, which further enhanced opportunities for communication and interaction.
| Author | : Jan Nagel |
| Publisher | : |
| Total Pages | : 374 |
| Release | : 2007 |
| Genre | : |
| ISBN | : 9781107095618 |
A self-contained account of the subject of algebraic cycles and motives as it stands.
| Author | : Bjorn Ian Dundas |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 228 |
| Release | : 2007-07-11 |
| Genre | : Mathematics |
| ISBN | : 3540458972 |
This book is based on lectures given at a summer school on motivic homotopy theory at the Sophus Lie Centre in Nordfjordeid, Norway, in August 2002. Aimed at graduate students in algebraic topology and algebraic geometry, it contains background material from both of these fields, as well as the foundations of motivic homotopy theory. It will serve as a good introduction as well as a convenient reference for a broad group of mathematicians to this important and fascinating new subject. Vladimir Voevodsky is one of the founders of the theory and received the Fields medal for his work, and the other authors have all done important work in the subject.
