| Résume | 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 these talks, we will translate their work back
into a statement suitable for (certain) automorphic functions, refining
the Langlands conjectures in this setting. Logically, this proceeds in
two steps. First, we will formulate a categorical conjecture suitable in
other geometric settings, including l-adic sheaves. Second, we will
explain the proof of the trace conjecture, which provides an
(unconditional) relationship between automorphic sheaves and automorphic
functions. This is joint work with Arinkin, Gaitsgory, Kazhdan,
Rozenblyum, and Varshavsky. |
