Quadratic torsion orders on Jacobian varieties
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914978369372160 |
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| author | Kuru, Hamide Sadek, Mohammad |
| author_facet | Kuru, Hamide Sadek, Mohammad |
| contents | We establish the existence of hyperelliptic curves of genus $g\ge 2$ defined over $\mathbb{Q}$ whose Jacobians possess rational torsion points of order $N$ where $N=4g^2+2g-2$ or $4g^2+ 2g -4$. For $N=2g^2+7g+1$, we introduce a $1$-parameter family of hyperelliptic curves of genus $g$ over $\mathbb{Q}$ with a rational torsion point of order $N$ on their Jacobians. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_14455 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Quadratic torsion orders on Jacobian varieties Kuru, Hamide Sadek, Mohammad Number Theory Algebraic Geometry We establish the existence of hyperelliptic curves of genus $g\ge 2$ defined over $\mathbb{Q}$ whose Jacobians possess rational torsion points of order $N$ where $N=4g^2+2g-2$ or $4g^2+ 2g -4$. For $N=2g^2+7g+1$, we introduce a $1$-parameter family of hyperelliptic curves of genus $g$ over $\mathbb{Q}$ with a rational torsion point of order $N$ on their Jacobians. |
| title | Quadratic torsion orders on Jacobian varieties |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2410.14455 |