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Modular functoriality in the Local Langlands Correspondence
We develop a theory of Smith--Treumann localization 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 $G$ an
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