Computing class groups and gonalities of algebraic curves over finite fields
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866915807406063616 |
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| author | Derickx, Maarten Terao, Kenji |
| author_facet | Derickx, Maarten Terao, Kenji |
| contents | We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The approach relies on introducing a precomputation step involving power series-expansions, which allows for an efficient amortized computation of large numbers of Riemann-Roch spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_17417 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Computing class groups and gonalities of algebraic curves over finite fields Derickx, Maarten Terao, Kenji Number Theory Algebraic Geometry 11G20, 14Q05, 14H40 We give practical algorithms for computing the divisor class group and the gonality of a curve over a finite field, achieving several orders of magnitude speedup over existing methods for sufficiently large genus or residue field. The approach relies on introducing a precomputation step involving power series-expansions, which allows for an efficient amortized computation of large numbers of Riemann-Roch spaces. |
| title | Computing class groups and gonalities of algebraic curves over finite fields |
| topic | Number Theory Algebraic Geometry 11G20, 14Q05, 14H40 |
| url | https://arxiv.org/abs/2602.17417 |