Wild Galois representations: elliptic curves over a 3-adic field
Volume 195 / 2020
Acta Arithmetica 195 (2020), 289-303
MSC: Primary 11G07; Secondary 11F80.
DOI: 10.4064/aa190423-9-1
Published online: 3 June 2020
Abstract
Given an elliptic curve $E$ over a local field $K$ with residue characteristic $3$, we investigate the action of the absolute Galois group of $K$ in the case of potentially good reduction. The hardest case is when the $\ell $-adic Galois representation attached to $E$ has non-cyclic inertia image, isomorphic to $C_3 \rtimes C_4$. In this work we describe such a representation explicitly.
