Wild Galois Representations: Elliptic curves over a $3$-adic field

Nirvana Coppola

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arXiv · 1812.05651

Wild Galois Representations: Elliptic curves over a $3$-adic field

Nirvana Coppola

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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. In particular the only not completely known case is that of the $\ell$-adic Galois representation attached to an elliptic curve such that the image of inertia is non-cyclic, and isomorphic to $C_3 \rtimes C_4$. In this work we describe such a representation explicitly.

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Nirvana Coppola. 2020-01-09. Wild Galois Representations: Elliptic curves over a $3$-adic field. https://arxiv.org/abs/1812.05651

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