Motives And Algebraic Cycles
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Motives And Algebraic Cycles
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Author : Rob de Jeu
language : en
Publisher: American Mathematical Soc.
Release Date : 2009
Motives And Algebraic Cycles written by Rob de Jeu and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Algebraic cycles categories.
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.
Algebraic Cycles And Motives Volume 1
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Author : Jan Nagel
language : en
Publisher: Cambridge University Press
Release Date : 2007-05-03
Algebraic Cycles And Motives Volume 1 written by Jan Nagel and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-05-03 with Mathematics categories.
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Mixed Motives And Algebraic K Theory
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Author : Uwe Jannsen
language : en
Publisher: Springer
Release Date : 2006-11-14
Mixed Motives And Algebraic K Theory written by Uwe Jannsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-14 with Mathematics categories.
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
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Author : Jan Nagel
language : en
Publisher:
Release Date : 2007
Algebraic Cycles And Motives written by Jan Nagel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algebraic cycles categories.
Algebraic Cycles And Motives
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Author : Jan Nagel
language : en
Publisher:
Release Date : 2007
Algebraic Cycles And Motives written by Jan Nagel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with categories.
A self-contained account of the subject of algebraic cycles and motives as it stands.
Algebraic Cycles And Motives
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Author : Jan Nagel
language : en
Publisher:
Release Date : 2007
Algebraic Cycles And Motives written by Jan Nagel and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Algebraic cycles categories.
A self-contained account of the subject of algebraic cycles and motives as it stands.
Lectures On Algebraic Cycles
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Author : Spencer Bloch
language : en
Publisher: Cambridge University Press
Release Date : 2010-07-22
Lectures On Algebraic Cycles written by Spencer Bloch and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-07-22 with Mathematics categories.
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.
Motives
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Author : Uwe Jannsen
language : en
Publisher: American Mathematical Soc.
Release Date : 1994
Motives written by Uwe Jannsen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Mathematics categories.
'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.
The Arithmetic And Geometry Of Algebraic Cycles
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Author : B. Brent Gordon
language : en
Publisher: Springer Science & Business Media
Release Date : 2000-02-29
The Arithmetic And Geometry Of Algebraic Cycles written by B. Brent Gordon and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-02-29 with Mathematics categories.
The subject of algebraic cycles has thrived through its interaction with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to such developments as a description of Chow groups in terms of algebraic K-theory, the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge and Tate, and the conjectures of Bloch and Beilinson. The immense recent progress in algebraic cycles, based on so many interactions with so many other areas of mathematics, has contributed to a considerable degree of inaccessibility, especially for graduate students. Even specialists in one approach to algebraic cycles may not understand other approaches well. This book offers students and specialists alike a broad perspective of algebraic cycles, presented from several viewpoints, including arithmetic, transcendental, topological, motives and K-theory methods. Topics include a discussion of the arithmetic Abel-Jacobi mapping, higher Abel-Jacobi regulator maps, polylogarithms and L-series, candidate Bloch-Beilinson filtrations, applications of Chern-Simons invariants to algebraic cycles via the study of algebraic vector bundles with algebraic connection, motivic cohomology, Chow groups of singular varieties, and recent progress on the Hodge and Tate conjectures for Abelian varieties.
Hodge Cycles Motives And Shimura Varieties
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Author : Pierre Deligne
language : en
Publisher: Springer
Release Date : 2009-03-20
Hodge Cycles Motives And Shimura Varieties written by Pierre Deligne and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-03-20 with Mathematics categories.