On close fields and the local Langlands correspondence
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866910520345362432 |
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| author | Li-Huerta, Siyan Daniel |
| author_facet | Li-Huerta, Siyan Daniel |
| contents | We prove that Fargues-Scholze's semisimplified local Langlands correspondence (for quasisplit groups) with $\overline{\mathbb{F}}_\ell$-coefficients is compatible with Deligne and Kazhdan's philosophy of close fields. From this, we deduce that the same holds with $\overline{\mathbb{Q}}_\ell$-coefficients after restricting to wild inertia, addressing questions of Gan-Harris-Sawin and Scholze. The proof involves constructing a moduli space of nonarchimedean local fields and then extending Fargues-Scholze's work to this context. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_07063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On close fields and the local Langlands correspondence Li-Huerta, Siyan Daniel Number Theory Algebraic Geometry Representation Theory 11S37 (Primary) 11F77, 14G45 (Secondary) We prove that Fargues-Scholze's semisimplified local Langlands correspondence (for quasisplit groups) with $\overline{\mathbb{F}}_\ell$-coefficients is compatible with Deligne and Kazhdan's philosophy of close fields. From this, we deduce that the same holds with $\overline{\mathbb{Q}}_\ell$-coefficients after restricting to wild inertia, addressing questions of Gan-Harris-Sawin and Scholze. The proof involves constructing a moduli space of nonarchimedean local fields and then extending Fargues-Scholze's work to this context. |
| title | On close fields and the local Langlands correspondence |
| topic | Number Theory Algebraic Geometry Representation Theory 11S37 (Primary) 11F77, 14G45 (Secondary) |
| url | https://arxiv.org/abs/2407.07063 |