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.

Regular and Irregular Holonomic D-Modules (London Mathematical Society Lecture Note Series, Series Number 433)

Science & Math

Kashiwara, Masaki

Schapira, Pierre

Mathematics

Cambridge University Press

Categories and sheaves appear almost frequently in contemporary advanced mathematics. This book covers categories, homological algebra and sheaves in a systematic manner starting from scratch and continuing with full proofs to the most recent results in the literature, and sometimes beyond. The authors present the general theory of categories and functors, emphasizing inductive and projective limits, tensor categories, representable functors, ind-objects and localization.

Categories and Sheaves (Grundlehren der mathematischen Wissenschaften, 332)

Springer

Sheaves on Manifolds: With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel (Grundlehren der mathematischen Wissenschaften)

Sheaf Theory is modern, active field of mathematics at the intersection of algebraic topology, algebraic geometry and partial differential equations. This volume offers a comprehensive and self-contained treatment of Sheaf Theory from the basis up, with emphasis on the microlocal point of view. From the reviews: "Clearly and precisely written, and contains many interesting ideas: it describes a whole, largely new branch of mathematics." –Bulletin of the L.M.S.

Sheaves on Manifolds: With a Short History. «Les débuts de la théorie des faisceaux». By Christian Houzel (Grundlehren der mathematischen Wissenschaften, 292)

Sheaves on Manifolds: With a Short History. Les débuts de la théorie des faisceaux. By Christian Houzel

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