Fields with few small points
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2023
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866910398663360512 |
|---|---|
| author | Hultberg, Nuno |
| author_facet | Hultberg, Nuno |
| contents | Let $X$ be a projective variety over a number field $K$ endowed with a height function associated to an ample line bundle on $X$. Given an algebraic extension $F$ of $K$ with a sufficiently big Northcott number, we can show that there are finitely many cycles in $X_{\bar{\mathbb{Q}}}$ of bounded degree defined over $F$. Fields $F$ with the required properties were explicitly constructed in arXiv:2107.09027 and arXiv:2204.04446, motivating our investigation. We point out explicit specializations to canonical heights associated to abelian varieties and selfmaps of $\mathbb{P}^n$. We apply similar methods to the study of CM-points. As a crucial tool, we introduce a refinement of Northcott's theorem. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_00297 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Fields with few small points Hultberg, Nuno Number Theory 11G50, 14G40, 11R04, 11G15 Let $X$ be a projective variety over a number field $K$ endowed with a height function associated to an ample line bundle on $X$. Given an algebraic extension $F$ of $K$ with a sufficiently big Northcott number, we can show that there are finitely many cycles in $X_{\bar{\mathbb{Q}}}$ of bounded degree defined over $F$. Fields $F$ with the required properties were explicitly constructed in arXiv:2107.09027 and arXiv:2204.04446, motivating our investigation. We point out explicit specializations to canonical heights associated to abelian varieties and selfmaps of $\mathbb{P}^n$. We apply similar methods to the study of CM-points. As a crucial tool, we introduce a refinement of Northcott's theorem. |
| title | Fields with few small points |
| topic | Number Theory 11G50, 14G40, 11R04, 11G15 |
| url | https://arxiv.org/abs/2307.00297 |