Algebraic D Modules

Author : S. C. Coutinho
Publisher : Cambridge University Press
Page : 223 pages
File Size : 47,6 Mb
Release : 1995-09-07
Category : Mathematics
ISBN : 9780521551199

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A Primer of Algebraic D-Modules by S. C. Coutinho Pdf

The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.

Author : Armand Borel
Publisher : Unknown
Page : 382 pages
File Size : 40,5 Mb
Release : 1987
Category : Mathematics
ISBN : UOM:49015000393570

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Algebraic D-modules by Armand Borel Pdf

Presented here are recent developments in the algebraic theory of D-modules. The book contains an exposition of the basic notions and operations of D-modules, of special features of coherent, holonomic, and regular holonomic D-modules, and of the Riemann-Hilbert correspondence. The theory of Algebraic D-modules has found remarkable applications outside of analysis proper, in particular to infinite dimensional representations of semisimple Lie groups, to representations of Weyl groups, and to algebraic geometry.

Author : Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 46,8 Mb
Release : 2007-11-07
Category : Mathematics
ISBN : 9780817643638

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D-Modules, Perverse Sheaves, and Representation Theory by Ryoshi Hotta,Toshiyuki Tanisaki Pdf

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.

Author : Masaki Kashiwara
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 52,9 Mb
Release : 2003
Category : Mathematics
ISBN : 0821827669

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D-modules and Microlocal Calculus by Masaki Kashiwara Pdf

Masaki Kashiwara is undoubtedly one of the masters of the theory of $D$-modules, and he has created a good, accessible entry point to the subject. The theory of $D$-modules is a very powerful point of view, bringing ideas from algebra and algebraic geometry to the analysis of systems of differential equations. It is often used in conjunction with microlocal analysis, as some of the important theorems are best stated or proved using these techniques. The theory has been used very successfully in applications to representation theory. Here, there is an emphasis on $b$-functions. These show up in various contexts: number theory, analysis, representation theory, and the geometry and invariants of prehomogeneous vector spaces. Some of the most important results on $b$-functions were obtained by Kashiwara. A hot topic from the mid '70s to mid '80s, it has now moved a bit more into the mainstream. Graduate students and research mathematicians will find that working on the subject in the two-decade interval has given Kashiwara a very good perspective for presenting the topic to the general mathematical public.

Author : Masaki Kashiwara,Pierre Schapira
Publisher : Cambridge University Press
Page : 119 pages
File Size : 49,5 Mb
Release : 2016-05-26
Category : Mathematics
ISBN : 9781316613450

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Regular and Irregular Holonomic D-Modules by Masaki Kashiwara,Pierre Schapira Pdf

A unified treatment of the Riemann-Hilbert correspondence for (not necessarily regular) holonomic D-modules using indsheaves.

Author : Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki
Publisher : Springer Science & Business Media
Page : 412 pages
File Size : 41,9 Mb
Release : 2007-10-12
Category : Mathematics
ISBN : 9780817645236

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D-Modules, Perverse Sheaves, and Representation Theory by Kiyoshi Takeuchi,Ryoshi Hotta,Toshiyuki Tanisaki Pdf

D-modules continues to be an active area of stimulating research in such mathematical areas as algebraic, analysis, differential equations, and representation theory. Key to D-modules, Perverse Sheaves, and Representation Theory is the authors' essential algebraic-analytic approach to the theory, which connects D-modules to representation theory and other areas of mathematics. To further aid the reader, and to make the work as self-contained as possible, appendices are provided as background for the theory of derived categories and algebraic varieties. The book is intended to serve graduate students in a classroom setting and as self-study for researchers in algebraic geometry, representation theory.

Author : Jan-Erik Björk
Publisher : Springer Science & Business Media
Page : 588 pages
File Size : 48,6 Mb
Release : 2013-06-29
Category : Mathematics
ISBN : 9789401707176

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Analytic D-Modules and Applications by Jan-Erik Björk Pdf

This is the first monograph to be published on analytic D-modules and it offers a complete and systematic treatment of the foundations together with a thorough discussion of such modern topics as the Riemann--Hilbert correspondence, Bernstein--Sata polynomials and a large variety of results concerning microdifferential analysis. Analytic D-module theory studies holomorphic differential systems on complex manifolds. It brings new insight and methods into many areas, such as infinite dimensional representations of Lie groups, asymptotic expansions of hypergeometric functions, intersection cohomology on Kahler manifolds and the calculus of residues in several complex variables. The book contains seven chapters and has an extensive appendix which is devoted to the most important tools which are used in D-module theory. This includes an account of sheaf theory in the context of derived categories, a detailed study of filtered non-commutative rings and homological algebra, and the basic material in symplectic geometry and stratifications on complex analytic sets. For graduate students and researchers.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 45,5 Mb
Release : 2024-06-28
Category : Electronic
ISBN : 9789814467964

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Algebraic Approach to Differential Equations by Anonim Pdf

Author : H. P. F. Swinnerton-Dyer
Publisher : Cambridge University Press
Page : 164 pages
File Size : 48,9 Mb
Release : 2001-02-22
Category : Mathematics
ISBN : 0521004233

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A Brief Guide to Algebraic Number Theory by H. P. F. Swinnerton-Dyer Pdf

Broad graduate-level account of Algebraic Number Theory, first published in 2001, including exercises, by a world-renowned author.

Author : David Eisenbud
Publisher : Springer Science & Business Media
Page : 784 pages
File Size : 40,7 Mb
Release : 2013-12-01
Category : Mathematics
ISBN : 9781461253501

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Commutative Algebra by David Eisenbud Pdf

This is a comprehensive review of commutative algebra, from localization and primary decomposition through dimension theory, homological methods, free resolutions and duality, emphasizing the origins of the ideas and their connections with other parts of mathematics. The book gives a concise treatment of Grobner basis theory and the constructive methods in commutative algebra and algebraic geometry that flow from it. Many exercises included.

Author : J. P. May
Publisher : University of Chicago Press
Page : 262 pages
File Size : 40,5 Mb
Release : 1999-09
Category : Mathematics
ISBN : 0226511839

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A Concise Course in Algebraic Topology by J. P. May Pdf

Algebraic topology is a basic part of modern mathematics, and some knowledge of this area is indispensable for any advanced work relating to geometry, including topology itself, differential geometry, algebraic geometry, and Lie groups. This book provides a detailed treatment of algebraic topology both for teachers of the subject and for advanced graduate students in mathematics either specializing in this area or continuing on to other fields. J. Peter May's approach reflects the enormous internal developments within algebraic topology over the past several decades, most of which are largely unknown to mathematicians in other fields. But he also retains the classical presentations of various topics where appropriate. Most chapters end with problems that further explore and refine the concepts presented. The final four chapters provide sketches of substantial areas of algebraic topology that are normally omitted from introductory texts, and the book concludes with a list of suggested readings for those interested in delving further into the field.

Author : Craig Huneke,Irena Swanson
Publisher : Cambridge University Press
Page : 446 pages
File Size : 43,9 Mb
Release : 2006-10-12
Category : Mathematics
ISBN : 9780521688604

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Integral Closure of Ideals, Rings, and Modules by Craig Huneke,Irena Swanson Pdf

Ideal for graduate students and researchers, this book presents a unified treatment of the central notions of integral closure.

Author : Raoul Bott,Loring W. Tu
Publisher : Springer Science & Business Media
Page : 319 pages
File Size : 51,9 Mb
Release : 2013-04-17
Category : Mathematics
ISBN : 9781475739510

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Differential Forms in Algebraic Topology by Raoul Bott,Loring W. Tu Pdf

Developed from a first-year graduate course in algebraic topology, this text is an informal introduction to some of the main ideas of contemporary homotopy and cohomology theory. The materials are structured around four core areas: de Rham theory, the Cech-de Rham complex, spectral sequences, and characteristic classes. By using the de Rham theory of differential forms as a prototype of cohomology, the machineries of algebraic topology are made easier to assimilate. With its stress on concreteness, motivation, and readability, this book is equally suitable for self-study and as a one-semester course in topology.

Author : F. S. Macaulay
Publisher : Cambridge University Press
Page : 148 pages
File Size : 47,6 Mb
Release : 1994-04-14
Category : Mathematics
ISBN : 0521455626

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The Algebraic Theory of Modular Systems by F. S. Macaulay Pdf

Originally published over 75 years ago, the wealth of thinking expounded here by Macaulay will still be a source of inspiration to all workers in commutative algebra.

Author : Michael F. Atiyah,I.G. MacDonald
Publisher : CRC Press
Page : 140 pages
File Size : 44,6 Mb
Release : 2018-03-09
Category : Mathematics
ISBN : 9780429973260

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Introduction To Commutative Algebra by Michael F. Atiyah,I.G. MacDonald Pdf

First Published in 2018. This book grew out of a course of lectures given to third year undergraduates at Oxford University and it has the modest aim of producing a rapid introduction to the subject. It is designed to be read by students who have had a first elementary course in general algebra. On the other hand, it is not intended as a substitute for the more voluminous tracts such as Zariski-Samuel or Bourbaki. We have concentrated on certain central topics, and large areas, such as field theory, are not touched. In content we cover rather more ground than Northcott and our treatment is substantially different in that, following the modern trend, we put more emphasis on modules and localization.