Regular and irregular holonomic D-modules / Masaki Kashiwara, Pierre Schapira.

Format:

Book

Author/Creator:

Kashiwara, Masaki, 1947- author.

Schapira, Pierre, 1943- author.

Series:

London Mathematical Society lecture note series ; 433.

London Mathematical Society lecture note series ; 433

Language:

English

Subjects (All):

D-modules.

Modules (Algebra).

Sheaf theory.

Geometry, Algebraic.

Physical Description:

1 online resource (vi, 111 pages) : digital, PDF file(s).

Other Title:

Regular & Irregular Holonomic D-Modules

Place of Publication:

Cambridge : Cambridge University Press, 2016.

Language Note:

English

Summary:

D-module theory is essentially the algebraic study of systems of linear partial differential equations. This book, the first devoted specifically to holonomic D-modules, provides a unified treatment of both regular and irregular D-modules. The authors begin by recalling the main results of the theory of indsheaves and subanalytic sheaves, explaining in detail the operations on D-modules and their tempered holomorphic solutions. As an application, they obtain the Riemann-Hilbert correspondence for regular holonomic D-modules. In the second part of the book the authors do the same for the sheaf of enhanced tempered solutions of (not necessarily regular) holonomic D-modules. Originating from a series of lectures given at the Institut des Hautes Études Scientifiques in Paris, this book is addressed to graduate students and researchers familiar with the language of sheaves and D-modules, in the derived sense.

Contents:

Cover ; Series information ; Title page ; Copyright information ; Table of contens ; Introduction; 1 A review on sheaves and D-modules; 2 Indsheaves; 3 Tempered solutions of D-modules; 4 Regular holonomic D-modules; 5 Indsheaves on bordered spaces; 6 Enhanced indsheaves; 7 Holonomic D-modules; 8 Integral transforms; References; Notations; Index; 1.1 Sheaves; 1.2 D-modules; 2.1 Ind-objects; 2.2 Indsheaves; 2.3 Ring action; 2.4 Sheaves on the subanalytic site; 2.5 Some classical sheaves on the subanalytic site; 3.1 Tempered de Rham and Sol functors; 3.2 Localization along a hypersurface

4.1 Regular normal form for holonomic modules4.2 Real blow up; 4.3 Regular Riemann-Hilbert correspondence; 4.4 Integral transforms with regular kernels; 4.5 Irregular D-modules: an example; 5.1 Bordered spaces; 5.2 Operations; 6.1 Tamarkin's construction; 6.2 Convolution products; 6.3 Enhanced indsheaves; 6.4 Operations on enhanced indsheaves; 6.5 Stable objects; 6.6 Constructible enhanced indsheaves; 6.7 Enhanced indsheaves with ring action; 7.1 Exponential D-modules; 7.2 Enhanced tempered holomorphic functions; 7.3 Enhanced de Rham and Sol functors

7.4 Ordinary linear differential equations and Stokes phenomena7.5 Normal form; 7.6 Enhanced de Rham functor on the real blow up; 7.7 De Rham functor: constructibility and duality; 7.8 Enhanced Riemann-Hilbert correspondence; 8.1 Integral transforms with irregular kernels; 8.2 Enhanced Fourier-Sato transform; 8.3 Laplace transform; 1.2.1 Basic constructions; 1.2.2 Filtrations and characteristic variety; 1.2.3 Internal operations; 1.2.4 De Rham and Spencer complexes; 1.2.5 External operations; 2.5.1 Tempered and Whitney functions and distributions; 2.5.2 Operations on tempered distributions

2.5.3 Whitney and tempered holomorphic functions2.5.4 Duality between Whitney and tempered functions

Notes:

Title from publisher's bibliographic system (viewed on 05 May 2016).

ISBN:

1-316-68342-7

1-316-68531-4

1-316-69155-1

1-316-68585-3

1-316-68666-3

1-316-67562-9