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Author: Jan Nagel
Publisher: Cambridge University Press
Published: 2007-05-03
Total Pages: 293
ISBN-13: 0521701740
DOWNLOAD EBOOK →This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Author: Rob de Jeu
Publisher: American Mathematical Soc.
Published: 2009
Total Pages: 354
ISBN-13: 0821844946
DOWNLOAD EBOOK →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.
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Publisher: American Mathematical Soc.
Published: 1994-02-28
Total Pages: 694
ISBN-13: 0821827987
DOWNLOAD EBOOK →'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: Spencer Bloch
Publisher: Cambridge University Press
Published: 2010-07-22
Total Pages: 155
ISBN-13: 1139487825
DOWNLOAD EBOOK →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
Publisher: Springer
Published: 2006-11-14
Total Pages: 260
ISBN-13: 3540469419
DOWNLOAD EBOOK →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: Burt Totaro
Publisher: Cambridge University Press
Published: 2014-06-26
Total Pages: 245
ISBN-13: 1107015774
DOWNLOAD EBOOK →This book presents a coherent suite of computational tools for the study of group cohomology algebraic cycles.
Author: Jan Nagel
Publisher: Cambridge University Press
Published: 2007-05-03
Total Pages: 360
ISBN-13: 0521701759
DOWNLOAD EBOOK →A self-contained account of the subject of algebraic cycles and motives as it stands.
Author: Bjorn Ian Dundas
Publisher: Springer Science & Business Media
Published: 2007-07-11
Total Pages: 228
ISBN-13: 3540458972
DOWNLOAD EBOOK →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.
Author: Annette Huber
Publisher: Springer
Published: 2017-03-08
Total Pages: 372
ISBN-13: 3319509268
DOWNLOAD EBOOK →This book casts the theory of periods of algebraic varieties in the natural setting of Madhav Nori’s abelian category of mixed motives. It develops Nori’s approach to mixed motives from scratch, thereby filling an important gap in the literature, and then explains the connection of mixed motives to periods, including a detailed account of the theory of period numbers in the sense of Kontsevich-Zagier and their structural properties. Period numbers are central to number theory and algebraic geometry, and also play an important role in other fields such as mathematical physics. There are long-standing conjectures about their transcendence properties, best understood in the language of cohomology of algebraic varieties or, more generally, motives. Readers of this book will discover that Nori’s unconditional construction of an abelian category of motives (over fields embeddable into the complex numbers) is particularly well suited for this purpose. Notably, Kontsevich's formal period algebra represents a torsor under the motivic Galois group in Nori's sense, and the period conjecture of Kontsevich and Zagier can be recast in this setting. Periods and Nori Motives is highly informative and will appeal to graduate students interested in algebraic geometry and number theory as well as researchers working in related fields. Containing relevant background material on topics such as singular cohomology, algebraic de Rham cohomology, diagram categories and rigid tensor categories, as well as many interesting examples, the overall presentation of this book is self-contained.
Author: Pierre Deligne
Publisher: Springer
Published: 2009-03-20
Total Pages: 423
ISBN-13: 3540389555
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