The Arithmetic and Geometry of Algebraic Cycles

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

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

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

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
Author: Jan Nagel
Publisher: Cambridge University Press
Total Pages: 293
Release: 2007-05-03
Genre: Mathematics
ISBN: 0521701740

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
Author: B. Brent Gordon
Publisher:
Total Pages: 432
Release: 2000
Genre: Algebraic cycles
ISBN: 9781470439385

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.

The Arithmetic and Geometry of Algebraic Cycles

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

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.

Algebraic Cycles, Sheaves, Shtukas, and Moduli

Algebraic Cycles, Sheaves, Shtukas, and Moduli
Author: Piotr Pragacz
Publisher: Springer Science & Business Media
Total Pages: 240
Release: 2008-03-12
Genre: Mathematics
ISBN: 3764385375

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.

Arithmetic Algebraic Geometry

Arithmetic Algebraic Geometry
Author: Jean-Louis Colliot-Thelene
Publisher: Springer
Total Pages: 218
Release: 2006-11-15
Genre: Mathematics
ISBN: 3540479090

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

Algebraic Cycles and Motives
Author: Jan Nagel
Publisher:
Total Pages: 292
Release: 2007
Genre: Algebraic cycles
ISBN: 9781107372436

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.

Algebraic Cycles and Hodge Theory

Algebraic Cycles and Hodge Theory
Author: Mark L. Green
Publisher: Springer
Total Pages: 281
Release: 2004-09-02
Genre: Mathematics
ISBN: 3540490469

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.