Regular and Irregular Holonomic D-Modules

Erscheinungsjahr 2016
ISBN: 978-1-316-61345-0
Verlag: Cambridge University Press

Buch, Englisch, Band 433, 117 Seiten, Format (B × H): 152 mm x 229 mm, Gewicht: 184 g

Reihe: London Mathematical Society Lecture Note Series

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.

Autoren/Hrsg.

Kashiwara, Masaki

Schapira, Pierre

Inhaltsverzeichnis

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.

Über Autor(innen)

Schapira, Pierre
Pierre Schapira is Professor Emeritus at the University of Paris VI. He is an internationally recognized specialist of algebraic analysis, the new branch of mathematics created by Mikio Sato in the 1970s.

Kashiwara, Masaki
Masaki Kashiwara is a project professor in the Research Institute for Mathematical Sciences at Kyoto University, Japan. He is an internationally recognized specialist of algebraic analysis, the new branch of mathematics created by Mikio Sato in the 1970s.