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

Research output: Contribution to journalArticle (Academic Journal)peer-review

1 Downloads (Pure)

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 languageEnglish
Number of pages10
JournalInternational Journal of Number Theory
Early online date10 Feb 2020
DOIs
Publication statusE-pub ahead of print - 10 Feb 2020

Keywords

  • elliptic curves
  • local fields
  • wild ramification
  • Galois representations

Fingerprint Dive into the research topics of 'Wild Galois representations: elliptic curves over a 2-adic field with non-abelian inertia action'. Together they form a unique fingerprint.

Cite this