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 Etudes
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.
General
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