Motives And Algebraic Cycles

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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.

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Genre : Mathematics
Author : Rob de Jeu
Publisher : American Mathematical Soc.
Release : 2009
File : 354 Pages
ISBN-13 : 9780821844946


Algebraic Cycles And Motives Volume 1

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

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Genre : Mathematics
Author : Jan Nagel
Publisher : Cambridge University Press
Release : 2007-05-03
File : 293 Pages
ISBN-13 : 9780521701747


Algebraic Cycles And Motives Volume 2

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A self-contained account of the subject of algebraic cycles and motives as it stands.

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Genre : Mathematics
Author : Jan Nagel
Publisher : Cambridge University Press
Release : 2007-05-03
File : 360 Pages
ISBN-13 : 9780521701754


Lectures On Algebraic Cycles

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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.

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Genre : Mathematics
Author : Spencer Bloch
Publisher : Cambridge University Press
Release : 2010-07-22
File : 155 Pages
ISBN-13 : 9781139487825


The Arithmetic And Geometry Of Algebraic Cycles

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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 description of Chow groups in terms of algebraic K-theory, the application of the Merkurjev-Suslin theorem to the arithmetic Abel-Jacobi mapping, progress on the celebrated conjectures of Hodge, and of Tate, which compute cycles classgroups respectively in terms of Hodge theory or as the invariants of a Galois group action on étale cohomology, the conjectures of Bloch and Beilinson, which explain the zero or pole of the $L$-function of a variety and interpret the leading non-zero coefficient of its Taylor expansion at a criticalpoint, in terms of arithmetic and geometric invariant of the variety and its cycle class groups.The immense recent progress in the theory of algebraic cycles is based on its many interactions with several other areas of mathematics. This conference was the first to focus on both arithmetic and geometric aspects of algebraic cycles. It brought together leading experts to speak from their various points of view. A unique opportunity was created to explore and view the depth and the breadth of the subject. This volume presents the intriguing results.

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Genre : Mathematics
Author : B. Brent Gordon
Publisher : American Mathematical Soc.
Release : 2000
File : 462 Pages
ISBN-13 : 9780821819548


Algebraic Cycles And Hodge Theory

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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.

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Genre : Mathematics
Author : Mark L. Green
Publisher : Springer
Release : 2004-09-02
File : 281 Pages
ISBN-13 : 9783540490463


Renormalization And Galois Theories

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This volume is the outcome of a CIRM Workshop on Renormalization and Galois Theories held in Luminy, France, in March 2006. The subject of this workshop was the interaction and relationship between four currently very active areas: renormalization in quantum field theory (QFT), differential Galois theory, noncommutative geometry, motives and Galois theory. The last decade has seen a burst of new techniques to cope with the various mathematical questions involved in QFT, with notably the development of a Hopf-algebraic approach and insights into the classes of numbers and special functions that systematically appear in the calculations of perturbative QFT (pQFT). The analysis of the ambiguities of resummation of the divergent series of pQFT, an old problem, has been renewed, using recent results on Gevrey asymptotics, generalized Borel summation, Stokes phenomenon and resurgent functions. The purpose of the present book is to highlight, in the context of renormalization, the convergence of these various themes, orchestrated by diverse Galois theories. It contains three lecture courses together with five research articles and will be useful to both researchers and graduate students in mathematics and physics.

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Genre : Mathematics
Author : Frédéric Fauvet
Publisher : European Mathematical Society
Release : 2009
File : 284 Pages
ISBN-13 : 3037190736


Transcendental Aspects Of Algebraic Cycles

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Lecture notes for graduates or researchers wishing to enter this modern field of research.

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Genre : Mathematics
Author : S. Müller-Stach
Publisher : Cambridge University Press
Release : 2004-04-20
File : 314 Pages
ISBN-13 : 0521545471


A Survey Of The Hodge Conjecture

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This book provides an introduction to a topic of central interest in transcendental algebraic geometry: the Hodge conjecture. Consisting of 15 lectures plus addenda and appendices, the volume is based on a series of lectures delivered by Professor Lewis at the Centre de Recherches Mathematiques (CRM). The book is a self-contained presentation, completely devoted to the Hodge conjecture and related topics. It includes many examples, and most results are completely proven or sketched. The motivation behind many of the results and background material is provided. This comprehensive approach to the book gives it a ``user-friendly'' style. Readers need not search elsewhere for various results. The book is suitable for use as a text for a topics course in algebraic geometry; includes an appendix by B. Brent Gordon.

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Genre : Mathematics
Author : James D. Lewis
Publisher : American Mathematical Soc.
Release : 1999-06-30
File : 386 Pages
ISBN-13 : 9781470428525


Hodge Cycles Motives And Shimura Varieties

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Genre : Mathematics
Author : Pierre Deligne
Publisher : Springer
Release : 2009-03-20
File : 423 Pages
ISBN-13 : 9783540389552