Abstract
In this paper we present a description of the $\ell$-adic 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 $\SL_2(\F_3)$, and in each case we need to distinguish whether the inertia degree of $K$ over $\Q_2$ is even or odd. The result presented here are being implemented in an algorithm to compute explicitly the Galois representation in these four cases.
Original language | English |
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Number of pages | 10 |
Journal | International Journal of Number Theory |
Early online date | 10 Feb 2020 |
DOIs | |
Publication status | E-pub ahead of print - 10 Feb 2020 |
Keywords
- elliptic curves
- local fields
- wild ramification
- Galois representations