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

2019/05/04 by Coppola, Nirvana · 4 citations
#11F80 #11G07 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1905.01462

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 Q₈ and SL₂(\mathbbF₃), and in each case we need to distinguish whether the inertia degree of K over ℚ₂ 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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• Inertial Types of Elliptic Curves Over ℚ_p²
• Local points on twists of X(p) with applications
• On 7-adic Galois representations for elliptic curves over ℚ
• Wild Galois representations: elliptic curves with wild cyclic reduction

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