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arXiv · 1507.01078

A Galois side analogue of a theorem of Bernstein

Manish Mishra
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Abstract

Let $G$ be a connected reductive group defined over a non archimedean local field $k$. A theorem of Bernstein states that for any compact open subgroup $K$ of $G(k)$, there are, up to unramified twists, only finitely many $K$-spherical supercuspidal representations of $G(k)$. We prove an analogous result on the Galois side of the Langlands correspondence.

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Manish Mishra. 2015-07-04. A Galois side analogue of a theorem of Bernstein. https://arxiv.org/abs/1507.01078

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