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Sheaf theory. --- Induction (Mathematics) --- Abelian categories. --- Sheaf theory --- Integral transforms --- D-modules --- Faisceaux, Théorie des. --- Transformations intégrales. --- D-modules, Théorie des. --- Faisceaux, Théorie des. --- Transformations intégrales. --- D-modules, Théorie des.

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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.

D-modules. --- Modules (Algebra) --- Sheaf theory. --- Geometry, Algebraic. --- Algebraic geometry --- Geometry --- Cohomology, Sheaf --- Sheaf cohomology --- Sheaves, Theory of --- Sheaves (Algebraic topology) --- Algebraic topology --- Finite number systems --- Modular systems (Algebra) --- Algebra --- Finite groups --- Rings (Algebra) --- D-modules, Théorie des. --- Modules (algèbre) --- Faisceaux, Théorie des. --- Géométrie algébrique.