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.

Full Product Details

Author:   Jan-Erik Björk
Publisher:   Springer
Imprint:   Springer
Edition:   Softcover reprint of the original 1st ed. 1993
Volume:   247
Dimensions:   Width: 17.00cm , Height: 3.00cm , Length: 24.40cm
Weight:   1.020kg
ISBN:  

9789048142385

ISBN 10:   9048142385
Pages:   581
Publication Date:   15 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational
Format:   Paperback
Publisher's Status:   Active
Availability:   Out of stock  
The supplier is temporarily out of stock of this item. It will be ordered for you on backorder and shipped when it becomes available.

Table of Contents

I. The sheaf DX and its modules.- II. Operations on D-modules.- III. Holonomic D-modules.- IV. Deligne modules.- V. Regular holonomic D-modules.- VI. b-functions.- VII. Distributions and regular holonomic systems.- VIII. Microdifferential operators.- A:I Derived Categories.- Summary.- A:I.1 The construction of derived categories.- A:I.2. Properties of derived categories.- A:I.3. Injective resolutions.- A:I.4. Spectral sequences.- A:II Sheaf Theory.- Summary.- A:II.1. The category of sheaves.- A:II.2. Operations on sheaves.- A:II.3. The derived category of sheaves.- A:II.4. Flabby sheaves.- A:II.5. Sheaves on paracompact manifolds.- A:II.6. Ringed spaces.- A:II.7. Derived categories of modules.- A:III Filtered rings.- Summary.- A:III.1. Filtered rings.- A:III.2. Filtered sheaves of rings.- A:III.3. Gabber’s Theorem.- A:IV Homological algebra.- Summary.- A:IV.1. Basic facts in homological algebra.- A:IV.2. Auslander regular rings.- A:IV.3. Commutative algebra.- A:IV.4. Filtered Auslander regular rings.- A:V Complex analysis.- Summary.- A:V.2. Analysis on complex manifolds.- A:V.4. The local Milnor fibrations.- A:VI Analytic geometry.- Summary.- A:VI.1. Subanalytic sets.- A:VII Symplectic analysis.- Summary.- A:VII.1. Symplectic algebra.- A:VII:3. Lagrangian varieties.- A:VII.4. Lagrangian varieties in generic position.- References.- List of notations.

Reviews

Author Information

Tab Content 6

Author Website:  

Countries Available

All regions