Corpus ID: 211266582

An Approach to the Characterization of the Local Langlands Correspondence

@article{Meli2020AnAT,
  title={An Approach to the Characterization of the Local Langlands Correspondence},
  author={Alexander Bertoloni Meli and Alex Youcis},
  journal={arXiv: Number Theory},
  year={2020}
}
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. 
1 Citations
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We prove that the supercuspidal cohomology of basic local Shimura varieties is concentrated in the middle degree, under a mild (and probably necessary) condition related to the local LanglandsExpand

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