# D-Modules

**Repository Path**: liqing-wang-cscs/d-modules

## Basic Information

- **Project Name**: D-Modules
- **Description**: A primer of algebraic D-modules.
- **Primary Language**: Unknown
- **License**: Not specified
- **Default Branch**: master
- **Homepage**: None
- **GVP Project**: No

## Statistics

- **Stars**: 0
- **Forks**: 0
- **Created**: 2025-06-15
- **Last Updated**: 2026-02-13

## Categories & Tags

**Categories**: Uncategorized

**Tags**: None

## README

## **A Primer of Algebraic D-Modules** by S. C. Coutinho. 

### Contents

1. The Weyl algebra
2. Ideal structure of the Weyl algebra
3. Rings of differential operators
4. Jacobian conjecture
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 D-modules
11. Characteristic varieties
12. Tensor products
13. External products
14. Invere images
15. Embedding
16. Direct images
17. Kashiwara's theorem
18. Preservation of holonomy
19. Stability of differential equations
20. Automated proof of identities

### Book cover
<img src="coutinho-book-cover.jpg" alt="" width="150" height="">


## **Algebraic D-Modules** by A. Borel

### Contents

1. Generalities of algebraic D-modules
2. Construction of resolutions. Two equivalences of categories
3. Left and right D-modules
4. Inverse images
5. Direct images 
6. Composition of direct images
7. Closed embeddings: inverse and direct images, the functor $\Gamma_{[Y]}$ 
8. Some applications
9. Coherent complexes
10. Holonomic complexes
11. Regular holonomic complexes
12. Preservation of regular holonomicity 
13. The de Rham functor
14. Statement of the main results. Some consequences
15. Proof of 14.5(1) 
16. Proof of 
17. Proof of 
18. Proof of 
19. Proof of 
20. Proof of 14.5(2), (3)
21. DR is an equivalence of categories
22. Regular holonomic modules and perverse sheaves

### Book cover
<img src="borel-book-cover.jpg" alt="" width="150" height="">