D-modules

Lectures: Tuesday 09.00-11.00, 7th October - 9th December. 

For those not at the University of Glasgow, the lectures are via the usual SMSTC Zoom link. For those at the University of Glasgow, lectures are in TBA. 

D-modules play a central role in representation theory and an important role in many aspects of algebraic geometry. This course, which assumes only a basic knowledge of algebraic geometry, will develop from scratch the theory of D-modules.

The end goal of the course is to understand the statement of the Riemann-Hilbert correspondence, giving an equivalence between the category of regular holonomic D-modules and the category of perverse sheaves (with complex coefficients) on a smooth complex algebraic variety.

Topics covered in the build-up to the equivalence include push-forward and pull-back of D-modules, good filtrations and characteristic varieties, holonomic D-modules, duality for holonomic D-modules and the classification of simple holonomic D-modules via minimal extensions.  

I will provide 5 exercise sheets and offer an office hour on Zoom for anyone who has questions, or wants to discuss any aspect of the course. These will be weekly, 3pm on Tuesday, from 14th October. 

Lecture notes and exercises will appear here in due course. 

1. Lecture one

2. Lecture two

3. Lecture three

4. Lecture four

5. Lecture five

6. Lecture six

7. Lecture seven

8. Lecture eight

9. Lecture nine

10. Lecture ten

Exercises:

1. Sheet 1

2. Sheet 2

3. Sheet 3

4. Sheet 4

5. Sheet 5

• Lecture notes