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The Arithmetic and Geometry of Algebraic Cycles

Author : B. Brent Gordon
Publisher : Springer Science & Business Media
ISBN 13 : 9780792361947
Total Pages : 652 pages
Book Rating : 4.3/5 (619 download)

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Book Synopsis The Arithmetic and Geometry of Algebraic Cycles by : B. Brent Gordon

Download or read book The Arithmetic and Geometry of Algebraic Cycles written by B. Brent Gordon and published by Springer Science & Business Media. This book was released on 2000-02-29 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Arithmetic and Geometry of Algebraic Cycles

Author : B. Brent Gordon
Publisher : Springer Science & Business Media
ISBN 13 : 9401140987
Total Pages : 631 pages
Book Rating : 4.4/5 (11 download)

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Book Synopsis The Arithmetic and Geometry of Algebraic Cycles by : B. Brent Gordon

Download or read book The Arithmetic and Geometry of Algebraic Cycles written by B. Brent Gordon and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 631 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

The Geometry of Algebraic Cycles

Author : Reza Akhtar
Publisher : American Mathematical Soc.
ISBN 13 : 0821851918
Total Pages : 202 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis The Geometry of Algebraic Cycles by : Reza Akhtar

Download or read book The Geometry of Algebraic Cycles written by Reza Akhtar and published by American Mathematical Soc.. This book was released on 2010 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: The subject of algebraic cycles has its roots in the study of divisors, extending as far back as the nineteenth century. Since then, and in particular in recent years, algebraic cycles have made a significant impact on many fields of mathematics, among them number theory, algebraic geometry, and mathematical physics. The present volume contains articles on all of the above aspects of algebraic cycles. It also contains a mixture of both research papers and expository articles, so that it would be of interest to both experts and beginners in the field.

The Arithmetic and Geometry of Algebraic Cycles

Author : B. Brent Gordon
Publisher :
ISBN 13 : 9781470439385
Total Pages : 432 pages
Book Rating : 4.4/5 (393 download)

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Book Synopsis The Arithmetic and Geometry of Algebraic Cycles by : B. Brent Gordon

Download or read book The Arithmetic and Geometry of Algebraic Cycles written by B. Brent Gordon and published by . This book was released on 2000 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt: The NATO ASI/CRM Summer School at Banff offered a unique, full, and in-depth account of the topic, ranging from introductory courses by leading experts to discussions of the latest developments by all participants. The papers have been organized into three categories: cohomological methods; Chow groups and motives; and arithmetic methods. As a subfield of algebraic geometry, the theory of algebraic cycles has gone through various interactions with algebraic K-theory, Hodge theory, arithmetic algebraic geometry, number theory, and topology. These interactions have led to developments such as a.

Arithmetic Algebraic Geometry

Author : Jean-Louis Colliot-Thelene
Publisher : Springer
ISBN 13 : 3540479090
Total Pages : 218 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Arithmetic Algebraic Geometry by : Jean-Louis Colliot-Thelene

Download or read book Arithmetic Algebraic Geometry written by Jean-Louis Colliot-Thelene and published by Springer. This book was released on 2006-11-15 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains three long lecture series by J.L. Colliot-Thelene, Kazuya Kato and P. Vojta. Their topics are respectively the connection between algebraic K-theory and the torsion algebraic cycles on an algebraic variety, a new approach to Iwasawa theory for Hasse-Weil L-function, and the applications of arithemetic geometry to Diophantine approximation. They contain many new results at a very advanced level, but also surveys of the state of the art on the subject with complete, detailed profs and a lot of background. Hence they can be useful to readers with very different background and experience. CONTENTS: J.L. Colliot-Thelene: Cycles algebriques de torsion et K-theorie algebrique.- K. Kato: Lectures on the approach to Iwasawa theory for Hasse-Weil L-functions.- P. Vojta: Applications of arithmetic algebraic geometry to diophantine approximations.

Algebraic Cycles and Motives

Author : Jan Nagel
Publisher :
ISBN 13 : 9781107365438
Total Pages : 292 pages
Book Rating : 4.3/5 (654 download)

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Book Synopsis Algebraic Cycles and Motives by : Jan Nagel

Download or read book Algebraic Cycles and Motives written by Jan Nagel and published by . This book was released on 2007 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic geometry is a central subfield of mathematics in which the study of cycles is an important theme. Alexander Grothendieck taught that algebraic cycles should be considered from a motivic point of view and in recent years this topic has spurred a lot of activity. This 2007 book is one of two volumes that provide a self-contained account of the subject. Together, the two books contain twenty-two contributions from leading figures in the field which survey the key research strands and present interesting new results. Topics discussed include: the study of algebraic cycles using Abel-Jacobi/regulator maps and normal functions; motives (Voevodsky's triangulated category of mixed motives, finite-dimensional motives); the conjectures of Bloch-Beilinson and Murre on filtrations on Chow groups and Bloch's conjecture. Researchers and students in complex algebraic geometry and arithmetic geometry will find much of interest here.

Recent Advances in Hodge Theory

Author : Matt Kerr
Publisher : Cambridge University Press
ISBN 13 : 110754629X
Total Pages : 533 pages
Book Rating : 4.1/5 (75 download)

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Book Synopsis Recent Advances in Hodge Theory by : Matt Kerr

Download or read book Recent Advances in Hodge Theory written by Matt Kerr and published by Cambridge University Press. This book was released on 2016-02-04 with total page 533 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Algebraic Cycles, Sheaves, Shtukas, and Moduli

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
ISBN 13 : 9783764385378
Total Pages : 236 pages
Book Rating : 4.3/5 (853 download)

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Book Synopsis Algebraic Cycles, Sheaves, Shtukas, and Moduli by : Piotr Pragacz

Download or read book Algebraic Cycles, Sheaves, Shtukas, and Moduli written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2008-03-12 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Articles examine the contributions of the great mathematician J. M. Hoene-Wronski. Although much of his work was dismissed during his lifetime, it is now recognized that his work offers valuable insight into the nature of mathematics. The book begins with elementary-level discussions and ends with discussions of current research. Most of the material has never been published before, offering fresh perspectives on Hoene-Wronski’s contributions.

The arithmetic and geometry of algebraic cycles : proceedings of the CRM Summer School June 7 - 19, 1998, Banff, Alberta, Canada

Author : B. Brent Gordon
Publisher :
ISBN 13 : 9780821819548
Total Pages : 432 pages
Book Rating : 4.8/5 (195 download)

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Book Synopsis The arithmetic and geometry of algebraic cycles : proceedings of the CRM Summer School June 7 - 19, 1998, Banff, Alberta, Canada by : B. Brent Gordon

Download or read book The arithmetic and geometry of algebraic cycles : proceedings of the CRM Summer School June 7 - 19, 1998, Banff, Alberta, Canada written by B. Brent Gordon and published by . This book was released on 2000 with total page 432 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Algebraic Cycles and Hodge Theory

Author : Mark L. Green
Publisher : Springer
ISBN 13 : 3540490469
Total Pages : 276 pages
Book Rating : 4.5/5 (44 download)

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Book Synopsis Algebraic Cycles and Hodge Theory by : Mark L. Green

Download or read book Algebraic Cycles and Hodge Theory written by Mark L. Green and published by Springer. This book was released on 2004-09-03 with total page 276 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Spencer Bloch
Publisher : Cambridge University Press
ISBN 13 : 1139487825
Total Pages : 155 pages
Book Rating : 4.1/5 (394 download)

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Book Synopsis Lectures on Algebraic Cycles by : Spencer Bloch

Download or read book Lectures on Algebraic Cycles written by Spencer Bloch and published by Cambridge University Press. This book was released on 2010-07-22 with total page 155 pages. 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.

Iterated Integrals and Cycles on Algebraic Manifolds

Author : Bruno Harris
Publisher : World Scientific
ISBN 13 : 9812562575
Total Pages : 121 pages
Book Rating : 4.8/5 (125 download)

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Book Synopsis Iterated Integrals and Cycles on Algebraic Manifolds by : Bruno Harris

Download or read book Iterated Integrals and Cycles on Algebraic Manifolds written by Bruno Harris and published by World Scientific. This book was released on 2004 with total page 121 pages. Available in PDF, EPUB and Kindle. Book excerpt: This subject has been of great interest both to topologists and tonumber theorists. The first part of this book describes some of thework of Kuo-Tsai Chen on iterated integrals and the fundamental groupof a manifold. The author attempts to make his exposition accessibleto beginning graduate students. He then proceeds to apply Chen''sconstructions to algebraic geometry, showing how this leads to someresults on algebraic cycles and the AbelOCoJacobihomomorphism. Finally, he presents a more general point of viewrelating Chen''s integrals to a generalization of the concept oflinking numbers, and ends up with a new invariant of homology classesin a projective algebraic manifold. The book is based on a coursegiven by the author at the Nankai Institute of Mathematics in the fallof 2001."

Algebraic Cycles and Motives

Author : Jan Nagel
Publisher :
ISBN 13 : 9781139882712
Total Pages : 359 pages
Book Rating : 4.8/5 (827 download)

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Book Synopsis Algebraic Cycles and Motives by : Jan Nagel

Download or read book Algebraic Cycles and Motives written by Jan Nagel and published by . This book was released on 2007 with total page 359 pages. Available in PDF, EPUB and Kindle. Book excerpt:

On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157)

Author : Mark L. Green
Publisher : Princeton University Press
ISBN 13 : 0691120447
Total Pages : 207 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) by : Mark L. Green

Download or read book On the Tangent Space to the Space of Algebraic Cycles on a Smooth Algebraic Variety. (AM-157) written by Mark L. Green and published by Princeton University Press. This book was released on 2005-01-09 with total page 207 pages. Available in PDF, EPUB and Kindle. Book excerpt: In recent years, considerable progress has been made in studying algebraic cycles using infinitesimal methods. These methods have usually been applied to Hodge-theoretic constructions such as the cycle class and the Abel-Jacobi map. Substantial advances have also occurred in the infinitesimal theory for subvarieties of a given smooth variety, centered around the normal bundle and the obstructions coming from the normal bundle's first cohomology group. Here, Mark Green and Phillip Griffiths set forth the initial stages of an infinitesimal theory for algebraic cycles. The book aims in part to understand the geometric basis and the limitations of Spencer Bloch's beautiful formula for the tangent space to Chow groups. Bloch's formula is motivated by algebraic K-theory and involves differentials over Q. The theory developed here is characterized by the appearance of arithmetic considerations even in the local infinitesimal theory of algebraic cycles. The map from the tangent space to the Hilbert scheme to the tangent space to algebraic cycles passes through a variant of an interesting construction in commutative algebra due to Angéniol and Lejeune-Jalabert. The link between the theory given here and Bloch's formula arises from an interpretation of the Cousin flasque resolution of differentials over Q as the tangent sequence to the Gersten resolution in algebraic K-theory. The case of 0-cycles on a surface is used for illustrative purposes to avoid undue technical complications.

Motives and Algebraic Cycles

Author : Rob de Jeu
Publisher : American Mathematical Soc.
ISBN 13 : 0821844946
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Motives and Algebraic Cycles by : Rob de Jeu

Download or read book Motives and Algebraic Cycles written by Rob de Jeu and published by American Mathematical Soc.. This book was released on 2009 with total page 354 pages. 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.

Local Systems in Algebraic-Arithmetic Geometry

Author : Hélène Esnault
Publisher : Springer Nature
ISBN 13 : 3031408403
Total Pages : 96 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Local Systems in Algebraic-Arithmetic Geometry by : Hélène Esnault

Download or read book Local Systems in Algebraic-Arithmetic Geometry written by Hélène Esnault and published by Springer Nature. This book was released on 2023-09-19 with total page 96 pages. Available in PDF, EPUB and Kindle. Book excerpt: The topological fundamental group of a smooth complex algebraic variety is poorly understood. One way to approach it is to consider its complex linear representations modulo conjugation, that is, its complex local systems. A fundamental problem is then to single out the complex points of such moduli spaces which correspond to geometric systems, and more generally to identify geometric subloci of the moduli space of local systems with special arithmetic properties. Deep conjectures have been made in relation to these problems. This book studies some consequences of these conjectures, notably density, integrality and crystallinity properties of some special loci. This monograph provides a unique compelling and concise overview of an active area of research and is useful to students looking to get into this area. It is of interest to a wide range of researchers and is a useful reference for newcomers and experts alike.

Topics in Transcendental Algebraic Geometry

Author : Phillip Griffiths
Publisher : Princeton University Press
ISBN 13 : 9780691083391
Total Pages : 332 pages
Book Rating : 4.0/5 (833 download)

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Book Synopsis Topics in Transcendental Algebraic Geometry by : Phillip Griffiths

Download or read book Topics in Transcendental Algebraic Geometry written by Phillip Griffiths and published by Princeton University Press. This book was released on 1984-06-21 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: "During 1981-1982 the Institute for Advanced Study held a special year on algebraic geometry. Naturally there were a number of seminars, and this volume is essentially the proceedings of one of these. The motif of the seminar was to explore the ways in which the recent developments in formal Hodge theory might be applied to problems in algebraic geometry."- introduction