GeNoCAS2023: Andreas Bode

Six operations and holonomicity for D-cap-modules on rigid analytic spaces

The study of D-modules, modules over a sheaf of differential operators, is commonly used as a geometric tool to understand representations. Ardakov-Wadsley introduced the theory of D-cap-modules on rigid analytic varieties as a p-adic analytic analogue, which provides insight in the locally analytic representation theory of p-adic groups. In this talk, I will discuss a derived-categorical framework for complete bornological D-cap-modules. This allows for the definition of six functors for D-cap-modules as well as a notion of holonomicity which behaves well with respect to these operations.