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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.
Product Details :
Genre |
: Mathematics |
Author |
: Rob de Jeu |
Publisher |
: American Mathematical Soc. |
Release |
: 2009 |
File |
: 354 Pages |
ISBN-13 |
: 9780821844946 |
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BOOK EXCERPT:
This 2007 book is a self-contained account of the subject of algebraic cycles and motives.
Product Details :
Genre |
: Mathematics |
Author |
: Jan Nagel |
Publisher |
: Cambridge University Press |
Release |
: 2007-05-03 |
File |
: 293 Pages |
ISBN-13 |
: 9780521701747 |
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BOOK EXCERPT:
A self-contained account of the subject of algebraic cycles and motives as it stands.
Product Details :
Genre |
: Mathematics |
Author |
: Jan Nagel |
Publisher |
: Cambridge University Press |
Release |
: 2007-05-03 |
File |
: 360 Pages |
ISBN-13 |
: 9780521701754 |
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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.
Product Details :
Genre |
: Mathematics |
Author |
: Spencer Bloch |
Publisher |
: Cambridge University Press |
Release |
: 2010-07-22 |
File |
: 155 Pages |
ISBN-13 |
: 9781139487825 |
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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 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.
Product Details :
Genre |
: Mathematics |
Author |
: B. Brent Gordon |
Publisher |
: American Mathematical Soc. |
Release |
: 2000 |
File |
: 462 Pages |
ISBN-13 |
: 9780821819548 |
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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.
Product Details :
Genre |
: Mathematics |
Author |
: Mark L. Green |
Publisher |
: Springer |
Release |
: 2004-09-02 |
File |
: 281 Pages |
ISBN-13 |
: 9783540490463 |
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BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: Frédéric Fauvet |
Publisher |
: European Mathematical Society |
Release |
: 2009 |
File |
: 284 Pages |
ISBN-13 |
: 3037190736 |
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BOOK EXCERPT:
Lecture notes for graduates or researchers wishing to enter this modern field of research.
Product Details :
Genre |
: Mathematics |
Author |
: S. Müller-Stach |
Publisher |
: Cambridge University Press |
Release |
: 2004-04-20 |
File |
: 314 Pages |
ISBN-13 |
: 0521545471 |
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BOOK EXCERPT:
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.
Product Details :
Genre |
: Mathematics |
Author |
: James D. Lewis |
Publisher |
: American Mathematical Soc. |
Release |
: 1999-06-30 |
File |
: 386 Pages |
ISBN-13 |
: 9781470428525 |
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BOOK EXCERPT:
Product Details :
Genre |
: Mathematics |
Author |
: Pierre Deligne |
Publisher |
: Springer |
Release |
: 2009-03-20 |
File |
: 423 Pages |
ISBN-13 |
: 9783540389552 |