Algebraic Cycles and Motives:

Author: Jan Nagel,Chris Peters

Publisher: Cambridge University Press

ISBN: 0521701740

Category: Mathematics

Page: 292

View: 7676

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

Motives and Algebraic Cycles

A Celebration in Honour of Spencer J. Bloch

Author: Spencer Bloch

Publisher: American Mathematical Soc.

ISBN: 0821844946

Category: Mathematics

Page: 336

View: 9718

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.

The Geometry of Algebraic Cycles

Proceedings of the Conference on Algebraic Cycles, Columbus, Ohio, March 25-29, 2008

Author: Reza Akhtar,Patrick Brosnan,Roy Joshua

Publisher: American Mathematical Soc.

ISBN: 0821851918

Category: Mathematics

Page: 187

View: 8156

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.

Transcendental Aspects of Algebraic Cycles

Proceedings of the Grenoble Summer School, 2001

Author: S. Müller-Stach,C. Peters

Publisher: Cambridge University Press

ISBN: 9780521545471

Category: Mathematics

Page: 290

View: 7820

This is a collection of lecture notes from the Summer School 'Cycles Algbriques; Aspects Transcendents, Grenoble 2001'. The topics range from introductory lectures on algebraic cycles to more advanced material. The advanced lectures are grouped under three headings: Lawson (co)homology, motives and motivic cohomology and Hodge theoretic invariants of cycles. Among the topics treated are: cycle spaces, Chow topology, morphic cohomology, Grothendieck motives, Chow-Knneth decompositions of the diagonal, motivic cohomology via higher Chow groups, the Hodge conjecture for certain fourfolds, an effective version of Nori's connectivity theorem, Beilinson's Hodge and Tate conjecture for open complete intersections. As the lectures were intended for non-specialists many examples have been included to illustrate the theory. As such this book will be ideal for graduate students or researchers seeking a modern introduction to the state-of-the-art theory in this subject.

Polynomials and the mod 2 Steenrod Algebra: Volume 1, The Peterson Hit Problem

Author: Grant Walker,Reginald M. W. Wood

Publisher: Cambridge University Press

ISBN: 1108359299

Category: Mathematics

Page: 346

View: 6322

This is the first book to link the mod 2 Steenrod algebra, a classical object of study in algebraic topology, with modular representations of matrix groups over the field F of two elements. The link is provided through a detailed study of Peterson's 'hit problem' concerning the action of the Steenrod algebra on polynomials, which remains unsolved except in special cases. The topics range from decompositions of integers as sums of 'powers of 2 minus 1', to Hopf algebras and the Steinberg representation of GL(n,F). Volume 1 develops the structure of the Steenrod algebra from an algebraic viewpoint and can be used as a graduate-level textbook. Volume 2 broadens the discussion to include modular representations of matrix groups.

Mathematical Reviews

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 9351

Recent Advances in Hodge Theory

Period Domains, Algebraic Cycles, and Arithmetic

Author: Matt Kerr,Gregory Pearlstein

Publisher: Cambridge University Press

ISBN: 110754629X

Category: Mathematics

Page: 528

View: 6621

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

Feynman Motives

Author: Matilde Marcolli

Publisher: World Scientific Publishing Company Incorporated

ISBN: 9789814304481

Category: Mathematics

Page: 220

View: 1069

This book presents recent and ongoing research work aimed at understanding the mysterious relation between the computations of Feynman integrals in perturbative quantum field theory and the theory of motives of algebraic varieties and their periods. One of the main questions in the field is understanding when the residues of Feynman integrals in perturbative quantum field theory evaluate to periods of mixed Tate motives. The question originates from the occurrence of multiple zeta values in Feynman integrals calculations observed by Broadhurst and Kreimer.Two different approaches to the subject are described. The first, a "bottom-up" approach, constructs explicit algebraic varieties and periods from Feynman graphs and parametric Feynman integrals. This approach, which grew out of work of Bloch–Enault–Keimer and was more recently developed in joint work of Paolo Aluffi and the author, leads to algebro-geometric and motivic versions of the Feynman rules of quantum field theory and concentrates on explicit constructions of motives and classes in the Grothendieck ring of varieties associated to Feynman integrals. While the varieties obtained in this way can be arbitrarily complicated as motives, the part of the cohomology that is involved in the Feynman integral computation might still be of the special mixed Tate kind. A second, "top-down" approach to the problem, developed in the work of Alain Connes and the author, consists of comparing a Tannakian category constructed out of the data of renormalization of perturbative scalar field theories, obtained in the form of a Riemann–Hilbert correspondence, with Tannakian categories of mixed Tate motives. The book draws connections between these two approaches and gives an overview of other ongoing directions of research in the field, outlining the many connections of perturbative quantum field theory and renormalization to motives, singularity theory, Hodge structures, arithmetic geometry, supermanifolds, algebraic and non-commutative geometry.The text is aimed at researchers in mathematical physics, high energy physics, number theory and algebraic geometry. Partly based on lecture notes for a graduate course given by the author at Caltech in the fall of 2008, it can also be used by graduate students interested in working in this area.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Anthony Hilton,John Talbot

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 8956

Number Theory and Algebraic Geometry

Author: Miles Reid,H. P. F. Swinnerton-Dyer,Alexei Skorobogatov

Publisher: Cambridge University Press

ISBN: 9780521545181

Category: Mathematics

Page: 300

View: 4357

This volume honors Sir Peter Swinnerton-Dyer's mathematical career spanning more than 60 years' of amazing creativity in number theory and algebraic geometry.

Arithmetic of Diagonal Hypersurfaces Over Finite Fields

Author: Fernando Q. Gouvêa,Noriko Yui

Publisher: Cambridge University Press

ISBN: 0521498341

Category: Mathematics

Page: 169

View: 868

This book is concerned with the arithmetic of diagonal hypersurfaces over finite fields.

Motivic Integration and its Interactions with Model Theory and Non-Archimedean Geometry:

Author: Raf Cluckers,Johannes Nicaise,Julien Sebag

Publisher: Cambridge University Press

ISBN: 1139501739

Category: Mathematics

Page: N.A

View: 5245

The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This second volume discusses various applications of non-Archimedean geometry, model theory and motivic integration and the interactions between these domains.

New Technical Books

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 7169

The Geometry of Moduli Spaces of Sheaves

A Publication of the Max-Planck-Institut für Mathematik, Bonn

Author: Daniel Huybrechts,Manfred Lehn

Publisher: Vieweg+Teubner Verlag

ISBN: 9783663116257

Category: Technology & Engineering

Page: 270

View: 9075

This book is intended to serve as an introduction to the theory of semistable sheaves and at the same time to provide a survey of recent research results on the geometry of moduli spaces. The first part introduces the basic concepts in the theory: Hilbert polynomial, slope, stability, Harder-Narasimhan filtration, Grothendieck's Quot-scheme. It presents detailed proofs of the Grauert-Mülich Theorem, the Bogomolov Inequality, the semistability of tensor products, and the boundedness of the family of semistable sheaves. It also gives a self-contained account of the construction of moduli spaces of semistable sheaves on a projective variety à la Gieseker, Maruyama, and Simpson. The second part presents some of the recent results of the geometry of moduli spaces of sheaves on an algebraic surface, following work of Mukai, O'Grady, Gieseker, Li and many others. In particular, moduli spaces of sheaves on K3 surfaces and determinant line bundles on the moduli spaces are treated in some detail. Other topics include the Serre correspondence, restriction of stable bundles to curves, symplectic structures, irreducibility and Kodaira-dimension of moduli spaces.

ABPR

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5801

Algebra für Einsteiger

Von der Gleichungsauflösung zur Galois-Theorie

Author: Jörg Bewersdorff

Publisher: Springer-Verlag

ISBN: 3658022620

Category: Mathematics

Page: 214

View: 7383

Dieses Buch ist eine leicht verständliche Einführung in die Algebra, die den historischen und konkreten Aspekt in den Vordergrund rückt. Der rote Faden ist eines der klassischen und fundamentalen Probleme der Algebra: Nachdem im 16. Jahrhundert allgemeine Lösungsformeln für Gleichungen dritten und vierten Grades gefunden wurden, schlugen entsprechende Bemühungen für Gleichungen fünften Grades fehl. Nach fast dreihundertjähriger Suche führte dies schließlich zur Begründung der so genannten Galois-Theorie: Mit ihrer Hilfe kann festgestellt werden, ob eine Gleichung mittels geschachtelter Wurzelausdrücke lösbar ist. Das Buch liefert eine gute Motivation für die moderne Galois-Theorie, die den Studierenden oft so abstrakt und schwer erscheint. In dieser Auflage wurde ein Kapitel ergänzt, in dem ein alternativer, auf Emil Artin zurückgehender Beweis des Hauptsatzes der Galois-Theorie wiedergegeben wird. Dieses Kapitel kann fast unabhängig von den anderen Kapiteln gelesen werden.

G-Functions and Geometry

A Publication of the Max-Planck-Institut für Mathematik, Bonn

Author: Yves André

Publisher: Springer-Verlag

ISBN: 366314108X

Category: Mathematics

Page: 232

View: 5943

Books in Print

Author: N.A

Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 5361