Regular and Irregular Holonomic D-Modules

Masaki Kashiwara, Pierre Schapira

• Publisher: Cambridge University Press
• Year: 2016
• Print ISBN: 9781316613450
• eBook ISBN: 9781316685310
• Topic: Mathematics
• Subtopic: Topology
• Index: Mathematics

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.

Table of 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