Orateur
Description
In this talk I'll propose a new way to organize discrete compound L-packets of a p-adic group G. Our packets include representations not only of inner twists of G but also of its elliptic twisted Levi subgroups, conjecturally realizing some version of loop Deligne–Lusztig induction or Yu's construction. The main idea is to replace Kottwitz's set with the non-basic cohomology of the Kaletha gerbe. This new cohomology set is much richer but turns out to carry many of the same structures as B(G), such as the Kottwitz and Newton maps. On the Galois side, we define a rigid enhancement for L-parameters and show that the resulting refined local Langlands conjectures reduce, à la Bertoloni Meli–Oi, to the basic rigid conjectures of Kaletha. This work is joint with Peter Dillery.
