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Author : Jan Nagel
Release : 2007-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 740/5 ( reviews)
Book Synopsis Algebraic Cycles and Motives: Volume 1 by : Jan Nagel
Download or read book Algebraic Cycles and Motives: Volume 1 written by Jan Nagel. This book was released on 2007-05-03. Available in PDF, EPUB and Kindle. Book excerpt: This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Author : Rob de Jeu
Release : 2009
Genre : Mathematics
Kind : eBook
Book Rating : 946/5 ( reviews)
Book Synopsis Motives and Algebraic Cycles by : Rob de Jeu
Download or read book Motives and Algebraic Cycles written by Rob de Jeu. This book was released on 2009. Available in PDF, EPUB and Kindle. Book excerpt: 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
Release : 2010-07-22
Genre : Mathematics
Kind : eBook
Book Rating : 825/5 ( reviews)
Book Synopsis Lectures on Algebraic Cycles by : Spencer Bloch
Download or read book Lectures on Algebraic Cycles written by Spencer Bloch. This book was released on 2010-07-22. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Uwe Jannsen
Release : 2006-11-14
Genre : Mathematics
Kind : eBook
Book Rating : 419/5 ( reviews)
Book Synopsis Mixed Motives and Algebraic K-Theory by : Uwe Jannsen
Download or read book Mixed Motives and Algebraic K-Theory written by Uwe Jannsen. This book was released on 2006-11-14. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jan Nagel
Release : 2007-05-03
Genre : Mathematics
Kind : eBook
Book Rating : 759/5 ( reviews)
Book Synopsis Algebraic Cycles and Motives: Volume 2 by : Jan Nagel
Download or read book Algebraic Cycles and Motives: Volume 2 written by Jan Nagel. This book was released on 2007-05-03. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of the subject of algebraic cycles and motives as it stands.
