Arithmetic bigness and a uniform Bogomolov-type result
Fuente:
arXiv
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2021
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866909184356777984 |
|---|---|
| author | Yuan, Xinyi |
| author_facet | Yuan, Xinyi |
| contents | In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2108_05625 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Arithmetic bigness and a uniform Bogomolov-type result Yuan, Xinyi Number Theory Algebraic Geometry 14G40, 11D45, 11G50 In this paper, we prove that the admissible canonical bundle of the universal family of curves is a big adelic line bundle, and apply it to prove a uniform Bogomolov-type theorem for curves over global fields of all characteristics. This gives a different approach to the uniform Mordell-Lang type of result of Dimitrov-Gao-Habegger and Kuhne. The treatment is based on the recent theory of adelic line bundles of Yuan-Zhang. |
| title | Arithmetic bigness and a uniform Bogomolov-type result |
| topic | Number Theory Algebraic Geometry 14G40, 11D45, 11G50 |
| url | https://arxiv.org/abs/2108.05625 |