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arXiv · 2407.07063

On close fields and the local Langlands correspondence

Siyan Daniel Li-Huerta
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Abstract

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.

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Siyan Daniel Li-Huerta. 2024-07-09. On close fields and the local Langlands correspondence. https://arxiv.org/abs/2407.07063

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