D-modules

Content

Please log in to view module content:

log in

Description

Tuesday 09.00-11.00

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 buildup 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.  

For those who require a grade from this course, the assessment will be to write up in latex one of the lectures. I will circulate a list of student names against lectures in due course. If you required a grade for the course but do not know what lecture you're writing up, please email me.

I will also 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.