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arXiv · 2210.02225

Three-Torsion Subgroups and Wild Conductors of Genus 3 Hyperelliptic Curves

Elvira Lupoian
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Abstract

We give a practical method for computing the 3-torsion subgroup of the Jacobian of a genus 3 hyperelliptic curve. We define a scheme for the 3-torsion points of the Jacobian and use complex approximations, homotopy continuation and lattice reduction to find precise expression for the 3-torsion. In the latter stages of the paper, we explain how the 3-torsion subgroup can be used to compute the wild part of the local exponent of the conductor at 2.

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Elvira Lupoian. 2022-10-05. Three-Torsion Subgroups and Wild Conductors of Genus 3 Hyperelliptic Curves. https://doi.org/10.1016/j.jnt.2025.04.015

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