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Journal of the Ramanujan Mathematical Society

Volume 30, Issue 4, December 2015  pp. 397–402.

A Galois side analogue of a theorem of Bernstein

Authors:  Manish Mishra
Author institution:Mathematics Center, Ruprecht-Karls-Universität Heidelberg D-69120, Heidelberg, Germany

Summary:  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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