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Tame categorical local Langlands correspondence (2504.07482v1)
Published 10 Apr 2025 in math.RT and math.AG
Abstract: In one of our previous articles, we outlined the formulation of a version of the categorical arithmetic local Langlands conjecture. The aims of this article are threefold. First, we provide a detailed account of one component of this conjecture: the local Langlands category. Second, we aim to prove this conjecture in the tame case for quasi-split unramified reductive groups. Finally, we will explore the first applications of such categorical equivalence.
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