On Galois representations of superelliptic curves

Ariel Pacetti; Angel Villanueva

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arXiv · 2012.09927

On Galois representations of superelliptic curves

Ariel Pacetti·Angel Villanueva

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Abstract

A superelliptic curve over a DVR ${\mathcal O}$ of residual characteristic $p$ is a curve given by an equation $C:y^n=f(x)$. The purpose of the present article is to describe the Galois representation attached to such a curve under the hypothesis that $f(x)$ has all its roots in the fraction field of ${\mathcal O}$ and that $p \nmid n$. Our results are inspired on the algorithm given in [BW17] but our description is given in terms of a cluster picture as defined in [DDMM18].

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Ariel Pacetti, Angel Villanueva. 2020-12-17. On Galois representations of superelliptic curves. https://arxiv.org/abs/2012.09927

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