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Regular and Irregular Holonomic D-Modules

Part of London Mathematical Society Lecture Note Series

  • Date Published: May 2016
  • availability: Available
  • format: Paperback
  • isbn: 9781316613450


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About the Authors
  • 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.

    • The first complete, unified treatment of holonomic D-modules
    • Treats both the regular (classical) case and the new irregular case
    • Provides an introduction to the theory of indsheaves, which will soon be an essential object of algebraic analysis
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    Product details

    • Date Published: May 2016
    • format: Paperback
    • isbn: 9781316613450
    • length: 117 pages
    • dimensions: 227 x 151 x 7 mm
    • weight: 0.19kg
    • availability: Available
  • Table of Contents

    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
    List of notations

  • Authors

    Masaki Kashiwara, Kyoto University, Japan
    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.

    Pierre Schapira, Université de Paris VI (Pierre et Marie Curie)
    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.

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