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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.

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.

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.

Algebraic Cycles and Motives: Volume 1

Author : Jan Nagel
Publisher : Cambridge University Press
ISBN 13 : 0521701740
Total Pages : 293 pages
Book Rating : 4.5/5 (217 download)

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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 and published by Cambridge University Press. This book was released on 2007-05-03 with total page 293 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 2007 book is a self-contained account of the subject of algebraic cycles and motives.

Algebraic Cycles and Hodge Theory

Author : Mark L. Green
Publisher :
ISBN 13 :
Total Pages : 275 pages
Book Rating : 4.:/5 (92 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 . This book was released on 1994 with total page 275 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.

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.

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.

Transcendental Aspects of Algebraic Cycles

Author : S. Müller-Stach
Publisher : Cambridge University Press
ISBN 13 : 9780521545471
Total Pages : 314 pages
Book Rating : 4.5/5 (454 download)

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Book Synopsis Transcendental Aspects of Algebraic Cycles by : S. Müller-Stach

Download or read book Transcendental Aspects of Algebraic Cycles written by S. Müller-Stach and published by Cambridge University Press. This book was released on 2004-04-20 with total page 314 pages. Available in PDF, EPUB and Kindle. Book excerpt: Lecture notes for graduates or researchers wishing to enter this modern field of research.

Algebraic cycles and motives

Author : Jan Nagel
Publisher :
ISBN 13 : 9781107095618
Total Pages : 359 pages
Book Rating : 4.0/5 (956 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: A self-contained account of the subject of algebraic cycles and motives as it stands.

Lectures on Algebraic Topology

Author : Sergeĭ Vladimirovich Matveev
Publisher : European Mathematical Society
ISBN 13 : 9783037190234
Total Pages : 112 pages
Book Rating : 4.1/5 (92 download)

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Book Synopsis Lectures on Algebraic Topology by : Sergeĭ Vladimirovich Matveev

Download or read book Lectures on Algebraic Topology written by Sergeĭ Vladimirovich Matveev and published by European Mathematical Society. This book was released on 2006 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic topology is the study of the global properties of spaces by means of algebra. It is an important branch of modern mathematics with a wide degree of applicability to other fields, including geometric topology, differential geometry, functional analysis, differential equations, algebraic geometry, number theory, and theoretical physics. This book provides an introduction to the basic concepts and methods of algebraic topology for the beginner. It presents elements of both homology theory and homotopy theory, and includes various applications. The author's intention is to rely on the geometric approach by appealing to the reader's own intuition to help understanding. The numerous illustrations in the text also serve this purpose. Two features make the text different from the standard literature: first, special attention is given to providing explicit algorithms for calculating the homology groups and for manipulating the fundamental groups. Second, the book contains many exercises, all of which are supplied with hints or solutions. This makes the book suitable for both classroom use and for independent study.

The Arithmetic and Geometry of Algebraic Cycles

Author : B. Brent Gordon
Publisher : American Mathematical Soc.
ISBN 13 : 9780821870204
Total Pages : 468 pages
Book Rating : 4.8/5 (72 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 American Mathematical Soc.. This book was released on 2000-01-01 with total page 468 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the June 1998 Summer School come 20 contributions that explore algebraic cycles (a subfield of algebraic geometry) from a variety of perspectives. The papers have been organized into sections on cohomological methods, Chow groups and motives, and arithmetic methods. Some specific topics include logarithmic Hodge structures and classifying spaces; Bloch's conjecture and the K-theory of projective surfaces; and torsion zero-cycles and the Abel-Jacobi map over the real numbers.

Hodge Theory (MN-49)

Author : Eduardo Cattani
Publisher : Princeton University Press
ISBN 13 : 1400851475
Total Pages : 608 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Hodge Theory (MN-49) by : Eduardo Cattani

Download or read book Hodge Theory (MN-49) written by Eduardo Cattani and published by Princeton University Press. This book was released on 2014-07-21 with total page 608 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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.

Arithmetic Algebraic Geometry

Author : Jean-Louis Colliot-Thelene
Publisher : Springer
ISBN 13 : 9783662170724
Total Pages : 226 pages
Book Rating : 4.1/5 (77 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 2014-03-12 with total page 226 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.

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.

Hodge Theory (MN-49)

Author : Eduardo Cattani
Publisher : Princeton University Press
ISBN 13 : 0691161348
Total Pages : 607 pages
Book Rating : 4.6/5 (911 download)

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Book Synopsis Hodge Theory (MN-49) by : Eduardo Cattani

Download or read book Hodge Theory (MN-49) written by Eduardo Cattani and published by Princeton University Press. This book was released on 2014-07-21 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Topics in Cohomological Studies of Algebraic Varieties

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
ISBN 13 : 3764373423
Total Pages : 321 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Topics in Cohomological Studies of Algebraic Varieties by : Piotr Pragacz

Download or read book Topics in Cohomological Studies of Algebraic Varieties written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis