Generalised Howe curves of genus five attaining the Serre bound
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909415372750848 |
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| author | Kawakita, Motoko Qiu |
| author_facet | Kawakita, Motoko Qiu |
| contents | We find that non-hyperelliptic generalised Howe curves and their twists of genus 5 attain the Hasse-Weil-Serre bound over some finite fields of order p, p^2 or p^3 for a prime p. We are able to decompose their Jacobians completely under certain assumptions and to determine the precise condition on the finite field over which they attain the Hasse-Weil-Serre bound. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_03071 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Generalised Howe curves of genus five attaining the Serre bound Kawakita, Motoko Qiu Algebraic Geometry 11G20, 14G05, 14G50 We find that non-hyperelliptic generalised Howe curves and their twists of genus 5 attain the Hasse-Weil-Serre bound over some finite fields of order p, p^2 or p^3 for a prime p. We are able to decompose their Jacobians completely under certain assumptions and to determine the precise condition on the finite field over which they attain the Hasse-Weil-Serre bound. |
| title | Generalised Howe curves of genus five attaining the Serre bound |
| topic | Algebraic Geometry 11G20, 14G05, 14G50 |
| url | https://arxiv.org/abs/2412.03071 |