A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866908698297761792 |
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| author | Mavraki, Niki Myrto Yap, Jit Wu |
| author_facet | Mavraki, Niki Myrto Yap, Jit Wu |
| contents | We prove a quantitative version of Zhang's fundamental inequality for heights attached to polarizable endomorphisms. As an application, we obtain a gap principle for the Néron-Tate height on abelian varieties over function fields of arbitrary transcendence degree and characteristic zero, extending the result of Gao-Ge-Kühne. We also establish instances of effective gap principles for regular polynomial endomorphisms of $\mathbb{P}^2$, in the sense that all constants can are explicit. These yield effective instances of uniformity in the dynamical Bogomolov conjecture in both the arithmetic and geometric settings, including examples in prime characteristic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_07655 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems Mavraki, Niki Myrto Yap, Jit Wu Number Theory Algebraic Geometry Dynamical Systems We prove a quantitative version of Zhang's fundamental inequality for heights attached to polarizable endomorphisms. As an application, we obtain a gap principle for the Néron-Tate height on abelian varieties over function fields of arbitrary transcendence degree and characteristic zero, extending the result of Gao-Ge-Kühne. We also establish instances of effective gap principles for regular polynomial endomorphisms of $\mathbb{P}^2$, in the sense that all constants can are explicit. These yield effective instances of uniformity in the dynamical Bogomolov conjecture in both the arithmetic and geometric settings, including examples in prime characteristic. |
| title | A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems |
| topic | Number Theory Algebraic Geometry Dynamical Systems |
| url | https://arxiv.org/abs/2512.07655 |