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LIFTING N-DIMENSIONAL GALOIS REPRESENTATIONS TO CHARACTERISTIC ZERO

Published online by Cambridge University Press:  20 June 2018

JAYANTA MANOHARMAYUM*
Affiliation:
School of Mathematics and Statistics, University of Sheffield, Sheffield S3 7RH, United Kingdom e-mail: J.Manoharmayum@sheffield.ac.uk
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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:GFGLN(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:GFGLN(W(k)) unramified outside finitely many primes with ρ ~ρ mod ℓ. Stronger results are presented for ρ:GGL3(k).

MSC classification

Type
Research Article
Copyright
Copyright © Glasgow Mathematical Journal Trust 2018 

References

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