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

Nirvana Coppola

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

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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
Publication statusE-pub ahead of print - 3 Jun 2020


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


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