On the Kottwitz conjecture for local Shimura varieties
OA Version
Citation
J Weinstein, Tasho Kaletha. "On the Kottwitz Conjecture for local Shimura varieties." Forum of Mathematics, Pi,
Abstract
Kottwitz’s conjecture describes the contribution of a supercuspidal represention to the cohomology of a local Shimura variety in terms of the local Langlands correspondence. Using a Lefschetz-Verdier fixedpoint formula, we prove a weakened generalized version of Kottwitz’s conjecture. The weakening comes from ignoring the action of the Weil group and only considering the actions of the groups G and Jb up to non-elliptic representations. The generalization is that we allow arbitrary connected reductive groups G and non-minuscule coweights µ.