Galois representations with big image in the general symplectic group GSp₄(ℤ_p)

2022/08/23 by Maletto, Simone
#11F80 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2208.11049

Abstract

Let p be an odd prime and e_p be its irregularity index. If 4e_p+8 <(p-1)/(2) we construct a Galois representation with image in the diagonal torus of \opGSp₄(\Fp) that lifts to a characteristic 0 representation unramified at all primes ℓ≠ p with image containing a finite index subgroup of \Symp.

Related

• p-adic Hodge parameters in the crystalline representations of GSp4
• On Galois representations with large image
• Tame Galois realizations of GSp₄(F_l) over Q
• A note on Galois representations valued in reductive groups with open image
• Galois representations for general symplectic groups