Three-Torsion Subgroups and Wild Conductors of Genus 3 Hyperelliptic Curves
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866916965533089792 |
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| author | Lupoian, Elvira |
| author_facet | Lupoian, Elvira |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_02225 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Three-Torsion Subgroups and Wild Conductors of Genus 3 Hyperelliptic Curves Lupoian, Elvira Number Theory 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. |
| title | Three-Torsion Subgroups and Wild Conductors of Genus 3 Hyperelliptic Curves |
| topic | Number Theory |
| url | https://arxiv.org/abs/2210.02225 |