On the local Langlands correspondence mod ell
Number Theory
2007-05-23 v1
Abstract
We prove that the reduction mod \ell of the local Langlands correspondence between supercuspidal representations of GL_n(F), where F is a finite extension of Q_p, and representations of the Galois group of F is well-defined. The results and methods of this paper have been used by Vigneras to give a proof of the ``local Langlands conjecture mod \ell'', that was proved earlier by her by different methods (local harmonic analysis mod \ell) for \ell>n. Unlike the local methods used earlier by Vigneras, our more global method also generalises well to the characteristic p case.
Cite
@article{arxiv.math/0011273,
title = {On the local Langlands correspondence mod ell},
author = {Chandrashekhar Khare},
journal= {arXiv preprint arXiv:math/0011273},
year = {2007}
}