Generic Vanishing for Holonomic D-modules

We construct an algebraic space parametrizing multiplicative line bundles with flat connection, known as character sheaves, on commutative algebraic groups. We then prove a generic vanishing theorem: for each holonomic D-module, there exists a dense open subset of this space over which the de Rham cohomology of twists by the corresponding character sheaves is concentrated in degree zero. As a key ingredient, we study extensions of abelian sheaves and various incarnations of Cartier duality.

This is a draft, so caveat emptor.