On the Kottwitz conjecture for local shtuka spaces

2017/09/19 by Kaletha, Tasho, Hansen, David, Weinstein, Jared · 1 citation
#11S37 #14G45 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1709.06651

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. A natural extension of this conjecture concerns Scholze's more general spaces of local shtukas. Using a new Lefschetz-Verdier trace formula for v-stacks, we prove the extended conjecture, disregarding the action of the Weil group, and modulo a virtual representation whose character vanishes on the locus of elliptic elements. As an application, we show that for an irreducible smooth representation of an inner form of GL_n, the L-parameter constructed by Fargues-Scholze agrees with the usual semisimplified parameter arising from local Langlands.

Cited by

• On the non-generic part of cohomology of compact unitary Shimura varieties of signature (1,n)

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