A primer of algebraic D-modules
著者
書誌事項
A primer of algebraic D-modules
（London Mathematical Society student texts, 33）
Cambridge University Press, 1995
- : hard
- : pbk
大学図書館所蔵 件 / 全72件
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410.8//L84//222715100122264,15100122272,
: pbk410.8//L84//746515100071586,15100074655 -
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注記
Includes bibliographical references (p. [197]-202) and index
内容説明・目次
内容説明
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.
目次
- 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.
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