A Primer of Algebraic D-Modules

London Mathematical Society Student Texts

by S.C. Coutinho

The theory of D-modules is a rich area of study combining ideas from algebra and differential equations, and it has significant applications to diverse areas such as singularity theory and representation theory. This book introduces D-modules and their applications avoiding all unnecessary over-sophistication. It is aimed at beginning graduate students and the approach taken is algebraic, concentrating on the role of the Weyl algebra. Very few prerequisites are assumed, and the book is virtually self-contained. Exercises are included at the end of each chapter and the reader is given ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.

220 pages, Kindle Edition

First published May 29, 1995

Reviews

[Andrew]

There are several expositions of D-modules, ranging from the extremely terse (Bernstein's lecture notes) to the very pedantic and thorough. But unlike all of these, this exposition uses almost no machinery (it is aimed at undergrads or first year grad students). On the one hand, that means it's not really an exposition of the theory: you can't define the direct image functor without derived categories. On the other, it's a helpful balance, and the concrete examples (such as adjoining the inverse of a polynomial to the polynomial ring to produce a holonomic D-module) are insightful and flow well.