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Regular and irregular holonomic D-modules. (English) Zbl 1354.32008
London Mathematical Society Lecture Note Series 433. Cambridge: Cambridge University Press (ISBN 978-1-316-61345-0/pbk; 978-1-316-67562-5/ebook). vi, 111 p. (2016).
Publisher’s description: 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.

##### MSC:
 32C38 Sheaves of differential operators and their modules, $$D$$-modules 14F10 Differentials and other special sheaves; D-modules; Bernstein-Sato ideals and polynomials 32-02 Research exposition (monographs, survey articles) pertaining to several complex variables and analytic spaces 14-02 Research exposition (monographs, survey articles) pertaining to algebraic geometry
##### Keywords:
holonomic D-modules; indsheaves; subanalytic sheaves
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