Wild Galois representations: elliptic curves over a 3-adic field

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

28 Downloads (Pure)

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. The hardest case is when the $\ell$-adic Galois representation attached to $E$ has non-cyclic inertia image, isomorphic to $C_3 \rtimes C_4$. In this work we describe such a representation explicitly.
Original languageEnglish
Number of pages15
JournalActa Arithmetica
Early online date3 Jun 2020
DOIs
Publication statusE-pub ahead of print - 3 Jun 2020

Keywords

  • Elliptic curves over local fields
  • Galois representations
  • Non-Abelian inertia action

Fingerprint Dive into the research topics of 'Wild Galois representations: elliptic curves over a 3-adic field'. Together they form a unique fingerprint.

Cite this