On the $L$-polynomials of curves over finite fields
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2018
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| _version_ | 1866913957062639616 |
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| author | Ballini, Francesco Lombardo, Davide Verzobio, Matteo |
| author_facet | Ballini, Francesco Lombardo, Davide Verzobio, Matteo |
| contents | We discuss, in a non-Archimedean setting, the distribution of the coefficients of $L$-polynomials of curves of genus $g$ over $\mathbb{F}_q$. Among other results, this allows us to prove that the $\mathbb{Q}$-vector space spanned by such characteristic polynomials has dimension $g+1$. We also state a conjecture about the Archimedean distribution of the number of rational points of curves over finite fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1807_07370 |
| institution | arXiv |
| publishDate | 2018 |
| record_format | arxiv |
| spellingShingle | On the $L$-polynomials of curves over finite fields Ballini, Francesco Lombardo, Davide Verzobio, Matteo Number Theory Algebraic Geometry 11F80, 11G20, 11G10 We discuss, in a non-Archimedean setting, the distribution of the coefficients of $L$-polynomials of curves of genus $g$ over $\mathbb{F}_q$. Among other results, this allows us to prove that the $\mathbb{Q}$-vector space spanned by such characteristic polynomials has dimension $g+1$. We also state a conjecture about the Archimedean distribution of the number of rational points of curves over finite fields. |
| title | On the $L$-polynomials of curves over finite fields |
| topic | Number Theory Algebraic Geometry 11F80, 11G20, 11G10 |
| url | https://arxiv.org/abs/1807.07370 |