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arXiv · 2312.12542

Modular functoriality in the Local Langlands Correspondence

Tony Feng
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Abstract

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.

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Tony Feng. 2023-12-19. Modular functoriality in the Local Langlands Correspondence. https://arxiv.org/abs/2312.12542

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