Reduction of Hyperelliptic Curves in Residue Characteristic 2

Tim Gehrunger; Richard Pink

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arXiv · 2404.14214

Reduction of Hyperelliptic Curves in Residue Characteristic 2

Tim Gehrunger·Richard Pink

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Abstract

Consider a hyperelliptic curve of genus $g$ over a field $K$ of characteristic zero. After extending $K$ we can view it as a marked curve with its $2g+2$ Weierstrass points. We present an explicit algorithm to compute the stable reduction of this marked curve for a valuation of residue characteristic $2$ over a finite extension of $K$. In the cases $g\le2$ we work out relatively simple conditions for the structure of this reduction.

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Tim Gehrunger, Richard Pink. 2024-04-22. Reduction of Hyperelliptic Curves in Residue Characteristic 2. https://arxiv.org/abs/2404.14214

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