[PDF] Classification Of Regular Holonomic D Modules eBook

Author : Masaki Kashiwara
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 19,44 MB
Release : 2003
Category : Mathematics
ISBN : 9780821827666

GET BOOK

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 : Armand Borel
Publisher :
Page : 382 pages
File Size : 44,15 MB
Release : 1987
Category : Mathematics
ISBN :

GET BOOK

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 : Masaki Kashiwara
Publisher : Cambridge University Press
Page : 119 pages
File Size : 41,99 MB
Release : 2016-05-26
Category : Mathematics
ISBN : 1316613453

GET BOOK

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

Author : Ryoshi Hotta
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 21,57 MB
Release : 2007-11-07
Category : Mathematics
ISBN : 081764363X

GET BOOK

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 : 48,64 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 9401707170

GET BOOK

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 : Masaki Kashiwara
Publisher : Walter de Gruyter
Page : 213 pages
File Size : 15,59 MB
Release : 2011-06-15
Category : Mathematics
ISBN : 3110856034

GET BOOK

The series is aimed specifically at publishing peer reviewed reviews and contributions presented at workshops and conferences. Each volume is associated with a particular conference, symposium or workshop. These events cover various topics within pure and applied mathematics and provide up-to-date coverage of new developments, methods and applications.

Author : S. C. Coutinho
Publisher : Cambridge University Press
Page : 223 pages
File Size : 24,5 MB
Release : 1995-09-07
Category : Mathematics
ISBN : 0521551196

GET BOOK

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.