| Autor: |
David Hansen, Tasho Kaletha, Jared Weinstein |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Forum of Mathematics, Pi, Vol 10 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
2050-5086 |
| DOI: |
10.1017/fmp.2022.7 |
| Popis: |
Kottwitz’s conjecture describes the contribution of a supercuspidal representation 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 $\operatorname {\mathrm {GL}}_n$ , the L-parameter constructed by Fargues–Scholze agrees with the usual semisimplified parameter arising from local Langlands. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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