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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 technicalities. The author takes an algebraic approach, concentrating on the role of the Weyl algebra. The author assumes very few prerequisites, and the book is virtually self-contained. The author includes exercises at the end of each chapter and gives the reader ample references to the more advanced literature. This is an excellent introduction to D-modules for all who are new to this area.Read more
- Only book on this subject at this level
- Ideal for people interested in the applications who only need to know the basic theory
- Based on courses given by the author in Brazil and Europe
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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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- Date Published: May 1995
- format: Paperback
- isbn: 9780521559089
- length: 220 pages
- dimensions: 229 x 152 x 13 mm
- weight: 0.33kg
- availability: Available
Table of Contents
1. The Weyl algebra
2. Ideal structure of the Weyl algebra
3. Rings of differential operators
4. Jacobian conjectures
5. Modules over the Weyl algebra
6. Differential equations
7. Graded and filtered modules
8. Noetherian rings and modules
9. Dimension and multiplicity
10. Holonomic modules
11. Characteristic varieties
12. Tensor products
13. External products
14. Inverse image
16. Direct images
17. Kashiwara's theorem
18. Preservation of holonomy
19. Stability of differential equations
20. Automatic proof of identities.
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