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| Format: | Preprint |
| Publié: |
2024
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| Accès en ligne: | https://arxiv.org/abs/2409.05796 |
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| _version_ | 1866912112786276352 |
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| author | Derickx, Maarten |
| author_facet | Derickx, Maarten |
| contents | A number field $K$ is called primitive if $\mathbb Q$ and $K$ are the only subfields of $K$. Let $X$ be a nice curve over $\mathbb Q$ of genus $g$. A point $P$ of degree $d$ on $X$ is called primitive if the field of definition $\mathbb Q(P)$ of the point is primitive. In this short note we prove that if $X$ has a divisor of degree $d> 2g$, then $X$ has infinitely many primitive points of degree $d$. This complements the results of Khawaja and Siksek that show that points of low degree are not primitive under certain conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_05796 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Large degree primitive points on curves Derickx, Maarten Number Theory 11G30 A number field $K$ is called primitive if $\mathbb Q$ and $K$ are the only subfields of $K$. Let $X$ be a nice curve over $\mathbb Q$ of genus $g$. A point $P$ of degree $d$ on $X$ is called primitive if the field of definition $\mathbb Q(P)$ of the point is primitive. In this short note we prove that if $X$ has a divisor of degree $d> 2g$, then $X$ has infinitely many primitive points of degree $d$. This complements the results of Khawaja and Siksek that show that points of low degree are not primitive under certain conditions. |
| title | Large degree primitive points on curves |
| topic | Number Theory 11G30 |
| url | https://arxiv.org/abs/2409.05796 |