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

Nirvana Coppola

doi:10.4064/aa190423-9-1

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

Nirvana Coppola

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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 language	English
Number of pages	15
Journal	Acta Arithmetica
Early online date	3 Jun 2020
DOIs	https://doi.org/10.4064/aa190423-9-1
Publication status	E-pub ahead of print - 3 Jun 2020

Keywords

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

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10.4064/aa190423-9-1

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This is the author accepted manuscript (AAM). The final published version (version of record) is available online via Polskiej Akademii Nauk, Instytut Matematyczny at https://www.impan.pl/en/publishing-house/journals-and-series/acta-arithmetica/online/113657/wild-galois-representations-elliptic-curves-over-a-3-adic-field . Please refer to any applicable terms of use of the publisher.
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title = "Wild Galois representations: elliptic curves over a 3-adic field",

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.",

keywords = "Elliptic curves over local fields, Galois representations, Non-Abelian inertia action",

author = "Nirvana Coppola",

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T2 - elliptic curves over a 3-adic field

AU - Coppola, Nirvana

PY - 2020/6/3

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N2 - 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.

AB - 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.

KW - Elliptic curves over local fields

KW - Galois representations

KW - Non-Abelian inertia action

U2 - 10.4064/aa190423-9-1

DO - 10.4064/aa190423-9-1

M3 - Article (Academic Journal)

SN - 0065-1036

JO - Acta Arithmetica

JF - Acta Arithmetica

ER -

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

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