The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles
Title The Arithmetic and Geometry of Algebraic Cycles PDF eBook
Author B. Brent Gordon
Publisher Springer Science & Business Media
Pages 652
Release 2000-02-29
Genre Mathematics
ISBN 9780792361947

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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 Geometry of Algebraic Cycles

The Geometry of Algebraic Cycles
Title The Geometry of Algebraic Cycles PDF eBook
Author Reza Akhtar
Publisher American Mathematical Soc.
Pages 202
Release 2010
Genre Mathematics
ISBN 0821851918

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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.

Algebraic Cycles and Motives: Volume 1

Algebraic Cycles and Motives: Volume 1
Title Algebraic Cycles and Motives: Volume 1 PDF eBook
Author Jan Nagel
Publisher Cambridge University Press
Pages 293
Release 2007-05-03
Genre Mathematics
ISBN 0521701740

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This 2007 book is a self-contained account of the subject of algebraic cycles and motives.

The Arithmetic and Geometry of Algebraic Cycles

The Arithmetic and Geometry of Algebraic Cycles
Title The Arithmetic and Geometry of Algebraic Cycles PDF eBook
Author B. Brent Gordon
Publisher Springer Science & Business Media
Pages 631
Release 2012-12-06
Genre Mathematics
ISBN 9401140987

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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.

Recent Advances in Hodge Theory

Recent Advances in Hodge Theory
Title Recent Advances in Hodge Theory PDF eBook
Author Matt Kerr
Publisher Cambridge University Press
Pages 533
Release 2016-02-04
Genre Mathematics
ISBN 110754629X

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Combines cutting-edge research and expository articles in Hodge theory. An essential reference for graduate students and researchers.

Calabi-Yau Varieties: Arithmetic, Geometry and Physics

Calabi-Yau Varieties: Arithmetic, Geometry and Physics
Title Calabi-Yau Varieties: Arithmetic, Geometry and Physics PDF eBook
Author Radu Laza
Publisher Springer
Pages 542
Release 2015-08-27
Genre Mathematics
ISBN 1493928309

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This volume presents a lively introduction to the rapidly developing and vast research areas surrounding Calabi–Yau varieties and string theory. With its coverage of the various perspectives of a wide area of topics such as Hodge theory, Gross–Siebert program, moduli problems, toric approach, and arithmetic aspects, the book gives a comprehensive overview of the current streams of mathematical research in the area. The contributions in this book are based on lectures that took place during workshops with the following thematic titles: “Modular Forms Around String Theory,” “Enumerative Geometry and Calabi–Yau Varieties,” “Physics Around Mirror Symmetry,” “Hodge Theory in String Theory.” The book is ideal for graduate students and researchers learning about Calabi–Yau varieties as well as physics students and string theorists who wish to learn the mathematics behind these varieties.

Rationality Problems in Algebraic Geometry

Rationality Problems in Algebraic Geometry
Title Rationality Problems in Algebraic Geometry PDF eBook
Author Arnaud Beauville
Publisher Springer
Pages 176
Release 2016-12-06
Genre Mathematics
ISBN 3319462091

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Providing an overview of the state of the art on rationality questions in algebraic geometry, this volume gives an update on the most recent developments. It offers a comprehensive introduction to this fascinating topic, and will certainly become an essential reference for anybody working in the field. Rationality problems are of fundamental importance both in algebra and algebraic geometry. Historically, rationality problems motivated significant developments in the theory of abelian integrals, Riemann surfaces and the Abel–Jacobi map, among other areas, and they have strong links with modern notions such as moduli spaces, Hodge theory, algebraic cycles and derived categories. This text is aimed at researchers and graduate students in algebraic geometry.