|Date: Monday, May 23, 2022
Location: Zoom: https://umich.zoom.us/j/7352196682?pwd=SThvaWpWOXlCSStYd2RmdDZXM3pSZz09 (PASSWORD: umichnt) Virtual (10:00 AM to 12:00 PM)
Title: Rigid inner forms over function fields
Abstract: We define a gerbe E over a (local or global) function field banded by a profinite group scheme whose set of G-torsors parametrizes all inner twists of an arbitrary connected reductive group G, generalizing the Kottwitz gerbe whose torsors parametrize extended pure inner forms of G. We discuss local and global duality results for these sets of torsors and use them to state conjectures regarding the local and global Langlands correspondence and endoscopy. Locally, we give a conjectural parametrization of L-packets and construct a Whittaker-normalized absolute transfer factor for an endoscopic datum. Globally, we relate these new local transfer factors to the adelic transfer factor and construct a pairing involving L-packets which is used in the conjectural multiplicity formula for discrete automorphic representations. A key part of the thesis is concerned with explicitly understanding G-torsors on the stack-theoretic gerbe E.
Peter's advisor is Tasho Kaletha.
Speaker: Peter Dillery