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arXiv · 1905.01462

Wild Galois representations: elliptic curves over a $2$-adic field with non-abelian inertia action

Nirvana Coppola
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Abstract

In this paper we present a description of the Galois representation attached to an elliptic curve defined over a $2$-adic field $K$, in the case where the image of inertia is non-abelian. There are two possibilities for the image of inertia, namely $Q_8$ and $SL_2(\mathbb{F}_3)$, and in each case we need to distinguish whether the inertia degree of $K$ over $\mathbb{Q}_2$ is even or odd. The result presented here can be implemented in an algorithm to compute explicitly the Galois representation in these four cases.

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Nirvana Coppola. 2019-05-04. Wild Galois representations: elliptic curves over a $2$-adic field with non-abelian inertia action. https://arxiv.org/abs/1905.01462

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