A Primer of Algebraic D-Modules
A Primer of Algebraic D-Modules
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.
- 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
Reviews & endorsements
"...an excellent textbook for a first encounter with D-module theory." Arno van den Essen, Mathematical Reviews
Product details
February 2011Adobe eBook Reader
9780511888649
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
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
- 15. Embeddings
- 16. Direct images
- 17. Kashiwara's theorem
- 18. Preservation of holonomy
- 19. Stability of differential equations
- 20. Automatic proof of identities.
