The integral Bernstein centre and local Langlands in families

For general linear groups over a p-adic field, local Langlands in families (established recently by Helm-Moss) provides a description of the integral Bernstein centre in terms of rings of functions on moduli spaces of Galois representations.   I will describe a conjectural generalisation of this picture to all split reductive p-adic groups and, at the end of the talk, I will discuss recent progress towards proving this conjecture in different special cases.  This is joint work with Jean-François Dat, David Helm, and Gil Moss.

vedi  Seminar Representation Theory