Modular functoriality in the Local Langlands Correspondence
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916369112498176 |
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| author | Feng, Tony |
| author_facet | Feng, Tony |
| contents | We develop a theory of Smith-Treumann localization and relative parity sheaves in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove some conjectures of Treumann-Venkatesh concerning mod-$\ell$ Local Langlands functoriality between a reductive group $G$ and its fixed subgroup under an order $\ell$ automorphism. As another application, we calculate the Fargues-Scholze parameters of mod-$\ell$ Howe-unramified toral representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_12542 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Modular functoriality in the Local Langlands Correspondence Feng, Tony Number Theory Representation Theory We develop a theory of Smith-Treumann localization and relative parity sheaves in the context of Fargues-Scholze's Geometrization of the Local Langlands Correspondence. We then apply this theory to prove some conjectures of Treumann-Venkatesh concerning mod-$\ell$ Local Langlands functoriality between a reductive group $G$ and its fixed subgroup under an order $\ell$ automorphism. As another application, we calculate the Fargues-Scholze parameters of mod-$\ell$ Howe-unramified toral representations. |
| title | Modular functoriality in the Local Langlands Correspondence |
| topic | Number Theory Representation Theory |
| url | https://arxiv.org/abs/2312.12542 |