Algebraic Cycles And Hodge Theory
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Algebraic Cycles And Hodge Theory
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Author : Mark L. Green
language : en
Publisher: Springer
Release Date : 2004-09-03
Algebraic Cycles And Hodge Theory written by Mark L. Green and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-09-03 with Mathematics categories.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
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 Theory Mn 49
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Author : Eduardo Cattani
language : en
Publisher: Princeton University Press
Release Date : 2014-07-21
Hodge Theory Mn 49 written by Eduardo Cattani and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-21 with Mathematics categories.
This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
The Arithmetic And Geometry Of Algebraic Cycles
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Author : B. Brent Gordon
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
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 2012-12-06 with Mathematics categories.
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.
Hodge Theory Mn 49
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Author : Eduardo Cattani
language : en
Publisher: Princeton University Press
Release Date : 2014-07-21
Hodge Theory Mn 49 written by Eduardo Cattani and has been published by Princeton University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-21 with Mathematics categories.
This book provides a comprehensive and up-to-date introduction to Hodge theory—one of the central and most vibrant areas of contemporary mathematics—from leading specialists on the subject. The topics range from the basic topology of algebraic varieties to the study of variations of mixed Hodge structure and the Hodge theory of maps. Of particular interest is the study of algebraic cycles, including the Hodge and Bloch-Beilinson Conjectures. Based on lectures delivered at the 2010 Summer School on Hodge Theory at the ICTP in Trieste, Italy, the book is intended for a broad group of students and researchers. The exposition is as accessible as possible and doesn't require a deep background. At the same time, the book presents some topics at the forefront of current research. The book is divided between introductory and advanced lectures. The introductory lectures address Kähler manifolds, variations of Hodge structure, mixed Hodge structures, the Hodge theory of maps, period domains and period mappings, algebraic cycles (up to and including the Bloch-Beilinson conjecture) and Chow groups, sheaf cohomology, and a new treatment of Grothendieck’s algebraic de Rham theorem. The advanced lectures address a Hodge-theoretic perspective on Shimura varieties, the spread philosophy in the study of algebraic cycles, absolute Hodge classes (including a new, self-contained proof of Deligne’s theorem on absolute Hodge cycles), and variation of mixed Hodge structures. The contributors include Patrick Brosnan, James Carlson, Eduardo Cattani, François Charles, Mark Andrea de Cataldo, Fouad El Zein, Mark L. Green, Phillip A. Griffiths, Matt Kerr, Lê Dũng Tráng, Luca Migliorini, Jacob P. Murre, Christian Schnell, and Loring W. Tu.
Recent Advances In Hodge Theory
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Author : Matt Kerr
language : en
Publisher: Cambridge University Press
Release Date : 2016-02-04
Recent Advances In Hodge Theory written by Matt Kerr 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 2016-02-04 with Mathematics categories.
Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.
Algebraic Cycles And Hodge Theory
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Author : Mark L. Green
language : en
Publisher: Springer
Release Date : 1994-12-16
Algebraic Cycles And Hodge Theory written by Mark L. Green and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-12-16 with Mathematics categories.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
Algebraic Cycles And Hodge Theory
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Author : Mark L. Green
language : en
Publisher:
Release Date : 1994
Algebraic Cycles And Hodge Theory written by Mark L. Green and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994 with Algebraic cycles categories.
The main goal of the CIME Summer School on "Algebraic Cycles and Hodge Theory" has been to gather the most active mathematicians in this area to make the point on the present state of the art. Thus the papers included in the proceedings are surveys and notes on the most important topics of this area of research. They include infinitesimal methods in Hodge theory; algebraic cycles and algebraic aspects of cohomology and k-theory, transcendental methods in the study of algebraic cycles.
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.
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.