Producing supersingular curves of genus five
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866918143896584192 |
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| author | Booher, Jeremy Pries, Rachel |
| author_facet | Booher, Jeremy Pries, Rachel |
| contents | For a prime $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. We produce this curve as an unramified double cover of a curve of genus three. We conjecture that the setting of unramified double covers of curves of genus three also produces supersingular curves of genus five when $p$ is congruent to one modulo four, and we computationally verify this conjecture for primes less than $100$. These results can be viewed as a generalization of work of Ekedahl and of Harashita, Kudo, and Senda. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_20262 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Producing supersingular curves of genus five Booher, Jeremy Pries, Rachel Number Theory Algebraic Geometry 2020 MSC primary: 11G20, 11M38, 14H30, 14H40. Secondary 11G10, 11G18, 14H10 For a prime $p$ congruent to three modulo four, we prove that there exists a smooth curve of genus five in characteristic $p$ that is supersingular. We produce this curve as an unramified double cover of a curve of genus three. We conjecture that the setting of unramified double covers of curves of genus three also produces supersingular curves of genus five when $p$ is congruent to one modulo four, and we computationally verify this conjecture for primes less than $100$. These results can be viewed as a generalization of work of Ekedahl and of Harashita, Kudo, and Senda. |
| title | Producing supersingular curves of genus five |
| topic | Number Theory Algebraic Geometry 2020 MSC primary: 11G20, 11M38, 14H30, 14H40. Secondary 11G10, 11G18, 14H10 |
| url | https://arxiv.org/abs/2410.20262 |