Local-global compatibility for l=p, II

2011/05/11 by Barnet-Lamb, Thomas, Gee, Toby, Geraghty, David +1
#11F33 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1105.2242

Abstract

We prove the compatibility at places dividing l of the local and global Langlands correspondences for the l-adic Galois representations associated to regular algebraic essentially (conjugate) self-dual cuspidal automorphic representations of GL_n over an imaginary CM or totally real field. We prove this compatibility up to semisimplification in all cases, and up to Frobenius semisimplification in the case of Shin-regular weight.

Related

• Local-global compatibility for l=p, I
• Compatibility of local and global Langlands correspondences
• The Local Langlands correspondence for \GL_n over p-adic fields
• Local-global compatibility for regular algebraic cuspidal automorphic representation when ℓ ≠ p
• A Rank-Two Case of Local-Global Compatibility for l = p