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An Approach to the Characterization of the Local Langlands Correspondence (2003.11484v2)
Published 25 Mar 2020 in math.NT and math.RT
Abstract: In this paper, we give a method for characterizing the local Langlands conjectures in the vein of Scholze's alternate proof of the local Langlands conjecture for $\mathrm{GL}_n$. More specifically, we show that if a local Langlands correspondence satisfies a Scholze--Shin equation, as in the paper of Scholze and Shin, in addition to the usual desiderata expected of such a correspondence then these properties uniquely characterize the correspondence.
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