Geodesic
LIFTING N-DIMENSIONAL GALOIS REPRESENTATIONS TO CHARACTERISTIC ZERO
Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 115-150

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DOI

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). 
MANOHARMAYUM, JAYANTA. LIFTING N-DIMENSIONAL GALOIS REPRESENTATIONS TO CHARACTERISTIC ZERO. Glasgow mathematical journal, Tome 61 (2019) no. 1, pp. 115-150. doi: 10.1017/S0017089518000149
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     author = {MANOHARMAYUM, JAYANTA},
     title = {LIFTING {N-DIMENSIONAL} {GALOIS} {REPRESENTATIONS} {TO} {CHARACTERISTIC} {ZERO}},
     journal = {Glasgow mathematical journal},
     pages = {115--150},
     year = {2019},
     volume = {61},
     number = {1},
     doi = {10.1017/S0017089518000149},
     url = {http://geodesic.mathdoc.fr/articles/10.1017/S0017089518000149/}
}
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