On Galois representations with large image

2021/04/06 by Maire, Christian
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2104.02505

Abstract

For every prime number p≥ 3 and every integer m≥ 1, we prove the existence of a continuous Galois representation ρ: G_ℚ → Gl_m(ℤ_p) which has open image and is unramified outside \p,∞\ (resp. outside \2,p,∞\) when p≡ 3 mod 4 (resp. p ≡ 1 mod 4).

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