Analytic D-Modules and Applications / Edition 1

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Overview

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.

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Product Details

  • ISBN-13: 9780792321149
  • Publisher: Springer Netherlands
  • Publication date: 1/31/1993
  • Series: Mathematics and Its Applications (closed) Series , #247
  • Edition description: 1993
  • Edition number: 1
  • Pages: 581
  • Product dimensions: 9.21 (w) x 6.14 (h) x 1.38 (d)

Table of Contents

Series editor's preface
Preface
Introduction
Ch. I The sheaf D[subscript X] and its modules
Ch. II Operations on D-modules
Ch. III Holonomic D-modules
Ch. IV Deligne modules
Ch. V Regular holonomic D-modules
Ch. VI b-functions
Ch. VII Distributions and regular holonomic systems
Ch. VIII Microdifferential operators
App. I Derived Categories
App. II Sheaf Theory
App. III Filtered rings
App. IV Homological algebra
App. V Complex analysis
App. VI Analytic geometry
App. VII Symplectic analysis
References
List of notations
Index
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