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Wild Galois representations: elliptic curves over a 3-adic field

Volume 195 / 2020

Nirvana Coppola Acta Arithmetica 195 (2020), 289-303 MSC: Primary 11G07; Secondary 11F80. DOI: 10.4064/aa190423-9-1 Published online: 3 June 2020


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.


  • Nirvana CoppolaSchool of Mathematics
    University of Bristol
    Fry Building, Woodland Road
    BS8 1UG Bristol, UK

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