On the local Langlands correspondence mod ell

Details On the local Langlands correspondence mod ell On the local Langlands correspondence mod ell

2000-11-27

arxiv.org/abs/math/0011273v1

Mathematics

Number Theory

Scientific paper

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.

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