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.