A Primer of Algebraic D-Modules

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Overview

Combining ideas from algebra and differential equations, the theory of D-modules is a rich area of study with significant applications to diverse areas such as singularity theory and representation theory. This text introduces D-modules and their applications.
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Editorial Reviews

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"...an excellent textbook for a first encounter with D-module theory." Arno van den Essen, Mathematical Reviews
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Product Details

Table of Contents

Preface
Introduction
Ch. 1 The Weyl algebra
Ch. 2 Ideal structure of the Weyl algebra
Ch. 3 Rings of differential operators
Ch. 4 Jacobian Conjecture
Ch. 5 Modules over the Weyl algebra
Ch. 6 Differential equations
Ch. 7 Graded and filtered modules
Ch. 8 Noetherian rings and modules
Ch. 9 Dimension and multiplicity
Ch. 10 Holonomic modules
Ch. 11 Characteristic varieties
Ch. 12 Tensor products
Ch. 13 External products
Ch. 14 Inverse Image
Ch. 15 Embeddings
Ch. 16 Direct images
Ch. 17 Kashiwara's theorem
Ch. 18 Preservation of holonomy
Ch. 19 Stability of differential equations
Ch. 20 Automatic proof of identities
Coda
Appendix 1. Defining the action of a module using generators
Appendix 2. Local inversion theorem
References
Index
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