D-modules on 1|1 supercurves

D-modules on 1|1 supercurves

It is known that to every (1|1)-dimensional supercurve X there is associated a dual supercurve X̂ , and a superdiagonal∆ ⊂ X× X̂ . We establish that the categories ofD-modules on X , X̂ and ∆ are equivalent. This follows from a more general result aboutD-modules and purely odd submersions. The equivalences preserve tensor products, and take vector bundles to vector bundles. Line bundles with conne...

Lectures on D-modules

These are lecture notes of a course given at the University of Chicago in Winter 1998. The purpose of the lectures is to give an introduction to the theory of modules over the (sheaf of) algebras of algebraic differential operators on a complex manifold. This theory was created about 15-20 years ago in the works of Beilinson-Bernstein and Kashiwara, and since then had a number of spectacular ap...

On Mirabolic D-modules

Let an algebraic group G act on X, a connected algebraic manifold, with finitely many orbits. For any Harish-Chandra pair (D , G) where D is a sheaf of twisted differential operators on X, we form a left ideal D g ⊂ D generated by the Lie algebra g = LieG. Then, D/D g is a holonomic D-module, and its restriction to a unique Zariski open dense G-orbit in X is a G-equivariant local system. We pro...

Notes on Equivariant D-modules

on direct sums of baer modules

the notion of baer modules was defined recently