D-modules on prestacks

This talk will be an introduction to the notion of D-modules on

prestacks. We will begin by discussing Grothendieck's definition of

crystals of quasi-coherent sheaves on a smooth scheme X, and briefly

indicate how the category of such objects is equivalent to that of

modules over the sheaf of differential operators on X. We will then

explain what we mean by a prestack and define the category of

quasi-coherent sheaves on them. Finally, we consider how the

crystalline approach may be used to give a suitable generalization

of D-modules to this derived setting.