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LIFTING N-DIMENSIONAL GALOIS REPRESENTATIONS TO CHARACTERISTIC ZERO

Part of: Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  20 June 2018

JAYANTA MANOHARMAYUM
JAYANTA MANOHARMAYUM*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom e-mail: [email protected]
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Abstract

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Let F be a number field, let N ≥ 3 be an integer, and let k be a finite field of characteristic ℓ. We show that if ρ:GF → GLN(k) is a continuous representation with image of ρ containing SLN(k) then, under moderate conditions at primes dividing ℓ∞, there is a continuous representation ρ:GF → GLN(W(k)) unramified outside finitely many primes with ρ ~ρ mod ℓ. Stronger results are presented for ρ:Gℚ → GL3(k).

MSC classification

Primary: 11F80: Galois representations
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 61 , Issue 1 , January 2019 , pp. 115 - 150
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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