| Résume | A local Langlands correspondence associates to each
irreducible admissible representation of a p-adic reductive group a
Galois theoretic object, namely an L parameter. In order to make the
correspondence bijective, one can enhance the target by additionally
recording a representation of a variant of the centralizer group of the
L parameter, and enhance the source by simultaneously considering
representations of inner twists of our p-adic group. I will discuss
recent work with Masao Oi on a certain statement of the Langlands
correspondence using the Kottwitz set and indicate what this might have
to do with the categorical conjecture of Fargues and Scholze. |
