# 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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