Organised by
Pol van Hoften .
This quarter we are studying moduli spaces of (local) Langlands parameters, following the paper of Dat-Helm-Kurinczuk-Moss, in order to understand the statement of a conjectural local Langlands correspondence "in families". We will also try to understand some of the results of Fargues-Scholze and perhaps briefly discuss their categorical version of the local Langlands correspondence, which implies a correspondence in families.
Seminar Schedule
-
(April 5th 2022): Introduction, overview and basics on Weil-Deligne representations (Pol). Notes .
-
(April 12th 2022): Moduli spaces of tame Langlands parameters (Vaughan).
-
(April 19th 2022): Reduction to tame parameters up to the proof of Theorem 3.4 of Dat-Helm-Kurinczuk-Moss (Ben). Notes .
-
(April 26th 2022): The proof of Theorem 3.4 of Dat-Helm-Kurinczuk-Moss (Sean).
-
(May 3rd 2022): Section 4 of Dat-Helm-Kurinczuk-Moss, with an emphasis on Theorem 4.13 and its proof (Connor)
-
(May 10th 2022): Connected components of moduli spaces of Langlands-parameters (Mark)
-
(May 17th 2022): Smooth representations of p-adic reductive groups I: Basics, parabolic induction, examples in depth zero (Thomas)
-
(May 24th 2022): Smooth representations of p-adic reductive groups II: Supercuspidal supports, blocks, and the Bernstein centre (Konstantin).
-
(May 31st 2022): Overview of the results of Fargues-Scholze and application to finiteness of Hecke algebras (Lie).
References