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arXiv · 2108.09492

Local Solubility of Hyperelliptic Curves

Omri Faraggi
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Abstract

We give a condition for a hyperelliptic curve $C$ over a local field $K$ to be locally soluble, on the condition that $C$ obtains semistable reduction after a tame extension of $K$, and that the residue field $k$ is sufficiently large relative to the genus of the curve. The condition is presented in terms of the cluster picture of $C$, a combinatorial object which determines much of the local arithmetic of $C$.

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Omri Faraggi. 2021-08-21. Local Solubility of Hyperelliptic Curves. https://arxiv.org/abs/2108.09492

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