[PDF] Regular And Irregular Holonomic D Modules eBook

Author : Masaki Kashiwara
Publisher : Cambridge University Press
Page : 119 pages
File Size : 41,19 MB
Release : 2016-05-26
Category : Mathematics
ISBN : 1316613453

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

Author : Masaki Kashiwara
Publisher : American Mathematical Soc.
Page : 276 pages
File Size : 33,78 MB
Release : 2003
Category : Mathematics
ISBN : 9780821827666

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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 : 31,33 MB
Release : 1987
Category : Mathematics
ISBN :

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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 : Kiyoshi Takeuchi
Publisher : Springer Science & Business Media
Page : 408 pages
File Size : 25,30 MB
Release : 2007-10-12
Category : Mathematics
ISBN : 0817645233

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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 : 49,29 MB
Release : 2013-06-29
Category : Mathematics
ISBN : 9401707170

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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 : Scott Balchin
Publisher : Cambridge University Press
Page : 357 pages
File Size : 50,19 MB
Release : 2021-11-18
Category : Mathematics
ISBN : 1108931944

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A collection of research papers, both new and expository, based on the interests of Professor J. P. C. Greenlees.

Author : Pieter Belmans
Publisher : Cambridge University Press
Page : 307 pages
File Size : 39,62 MB
Release : 2022-10-31
Category : Mathematics
ISBN : 1009054856

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A collection of expository articles on modern topics in algebraic geometry, focusing on the geometry of algebraic spaces and stacks.

Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 242 pages
File Size : 49,30 MB
Release : 2022-04-28
Category : Mathematics
ISBN : 1009050036

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This book provides the first thorough treatment of effective results and methods for Diophantine equations over finitely generated domains. Compiling diverse results and techniques from papers written in recent decades, the text includes an in-depth analysis of classical equations including unit equations, Thue equations, hyper- and superelliptic equations, the Catalan equation, discriminant equations and decomposable form equations. The majority of results are proved in a quantitative form, giving effective bounds on the sizes of the solutions. The necessary techniques from Diophantine approximation and commutative algebra are all explained in detail without requiring any specialized knowledge on the topic, enabling readers from beginning graduate students to experts to prove effective finiteness results for various further classes of Diophantine equations.