Regular and Irregular Holonomic D-Modules

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

Masaki Kashiwara (Author), Pierre Schapira (Author)

9781316613450, Cambridge University Press

Paperback / softback, published 26 May 2016

117 pages
22.7 x 15.1 x 0.7 cm, 0.19 kg

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.

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
List of notations
Index.

Subject Areas: Mathematical physics [PHU], Topology [PBP], Algebraic geometry [PBMW], Differential calculus & equations [PBKJ]