Journal of the Ramanujan Mathematical Society

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A Galois Side Analogue of a Theorem of Bernstein


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1 Mathematics Center, Ruprecht-Karls-Universitat Heidelberg D-69120, Heidelberg, Germany
     

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Let G be a connected reductive group defined over a non archimedean local field k. A theorem of Bernstein states that for any compact subgroup K of G(k), there are, upto 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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  • A Galois Side Analogue of a Theorem of Bernstein

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Authors

Manish Mishra
Mathematics Center, Ruprecht-Karls-Universitat Heidelberg D-69120, Heidelberg, Germany

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 subgroup K of G(k), there are, upto 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.