In celebrated work, Beilinson-Drinfeld formulated a categorical analogue of the Langlands program for unramified automorphic forms. Their conjecture has appeared specialized to the setting of algebraic D-modules: non-holonomic D-modules play a prominent role in known constructions.
In this talk, we will discuss a categorical conjecture suitable in other geometric settings, including l-adic sheaves. One of the main constructions is a suitable moduli space of local systems. We will also discuss applications to unramified automorphic forms for function fields. This is joint work with Arinkin, Gaitsgory, Kazhdan, Rozenblyum, and Varshavsky.