The conjectural local Langlands correspondence connects representations of p-adic groups to certain representations of Galois groups of local fields called Langlands parameters. In recent joint work with Dat, Helm, and Moss, we have constructed moduli spaces of Langlands parameters over \( \mathbb{Z}[1/p]\) and studied their geometry. We expect this geometry is reflected in the representation theory of the p-adic group. Our main conjecture “local Langlands in families” describes the GIT quotient of the moduli space of Langlands parameters in terms of the centre of the category of representations of the p-adic group generalising a theorem of Helm-Moss for GL(n). I will explain how after inverting the "non-banal primes" one can prove this conjecture for the local Langlands correspondence for classical groups of Arthur and others.
Local Langlands in families for classical groups
12.10.2021 13:15 - 14:45
Organiser:
H. Grobner, A. Minguez-Espallargas, A. Mellit
Location: