Curves with prescribed rational points
Fuente:
arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866929568925876224 |
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| author | Santicola, Katerina |
| author_facet | Santicola, Katerina |
| contents | Given a smooth curve $C/\mathbb{Q}$ with genus $\geq 2$, we know by Faltings' Theorem that $C(\mathbb{Q})$ is finite. Here we ask the reverse question: given a finite set of rational points $S\subseteq \mathbb{P}^n(\mathbb{Q})$, does there exist a smooth curve $C/\mathbb{Q}$ contained in $\mathbb{P}^n$ such that $C(\mathbb{Q})=S$? We answer this question in the affirmative by providing an effective algorithm for constructing such a curve. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_09396 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Curves with prescribed rational points Santicola, Katerina Number Theory Given a smooth curve $C/\mathbb{Q}$ with genus $\geq 2$, we know by Faltings' Theorem that $C(\mathbb{Q})$ is finite. Here we ask the reverse question: given a finite set of rational points $S\subseteq \mathbb{P}^n(\mathbb{Q})$, does there exist a smooth curve $C/\mathbb{Q}$ contained in $\mathbb{P}^n$ such that $C(\mathbb{Q})=S$? We answer this question in the affirmative by providing an effective algorithm for constructing such a curve. |
| title | Curves with prescribed rational points |
| topic | Number Theory |
| url | https://arxiv.org/abs/2401.09396 |