On the Kottwitz conjecture for local Shimura varieties
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Citation (published version)J Weinstein, Tasho Kaletha. "On the Kottwitz Conjecture for local Shimura varieties." Forum of Mathematics, Pi,
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.