On the local Langlands correspondence mod ell

2000/11/27 by Chandrashekhar Khare, Khare, Chandrashekhar
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.math/0011273

arxiv created 2000/11/27 · arxiv updated 2009/12/01

Abstract

We prove that the reduction mod ℓ 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 ℓ'', that was proved earlier by her by different methods (local harmonic analysis mod ℓ) for ℓ>n. Unlike the local methods used earlier by Vigneras, our more global method also generalises well to the characteristic p case.

Related

• Local Langlands correspondence for regular supercuspidal representations of GL(n)
• The local Langlands correspondence for GL_n in families
• Local Jacquet-Langlands correspondence for regular supercuspidal representations
• Compatibility of local and global Langlands correspondences
• On the local Langlands correspondence