Automorphic gluing in geometric Langlands via sheaves of categories with Hochschild cochains action

Seminar series

Geometry and Analysis Seminar

Date

Mon, 24 Oct 2016

Time

14:15 - 15:15

Location

Speaker

Dario Beraldo

Organisation

Oxford

I will define the notion of "sheaf of categories with a local action of Hochschild cochains" over a stack. (This notion is analogous to D-modules, in the same way as the notion of "sheaf of categories" is analogous to quasi-coherent sheaves.) I will prove that both categories appearing in geometric Langlands carry this structure over the stack of de Rham {\check{G}}-local systems. Using this, I will explain how to glue D-mod(Bun_G) out of *tempered* D-modules associated to smaller Levi subgroups of G.