Lifting N-dimensional Galois representations to characteristic zero

2013/01/29 by Jayanta Manoharmayum, Manoharmayum, Jayanta
Mathematics · #11F80 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Analytic Number Theory Research #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11F80

paper · pdf · doi:10.48550/arxiv.1301.7103

28 pages

arxiv created 2013/01/29 · openalex publication_date 2013/01/29 · arxiv updated 2013/01/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \rb:G_F\longrightarrow GL_N(k) is a continuous representation with image of \rb containing SL_N(k) then, under moderate conditions at primes dividing ℓ∞, there is a continuous representation ρ:G_F\longrightarrow GL_N(W(k)) unramified outside finitely many primes with \rb∼ρ\modℓ.

Related

• On Galois representations with large image
• Comparing Galois representations in the residually reducible case
• Lifting Galois representations to ramified coefficient fields
• The lifting problem for Galois representations
• Images of Galois representations in mod p Hecke algebras