A counting argument for the geometric Bombieri-Lang conjecture on ramified covers of abelian varieties
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908859815165952 |
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| author | Gao, Guoquan |
| author_facet | Gao, Guoquan |
| contents | We prove the geometric Bombieri-Lang conjecture for projective varieties which have finite maps to abelian varieties over function fields of characteristic 0. This generalizes the recent results of Xie-Yuan, which require either the hyperbolicity assumption or the non-isotriviality assumption. The proof builds upon their strategy for constructing entire curves, yet hinges crucially on a new counting argument and draws substantially on tools from algebraic geometry and Nevanlinna theory to overcome various technical difficulties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_17010 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A counting argument for the geometric Bombieri-Lang conjecture on ramified covers of abelian varieties Gao, Guoquan Number Theory Algebraic Geometry Complex Variables 14G05, 11G35, 11J97, 32H30 We prove the geometric Bombieri-Lang conjecture for projective varieties which have finite maps to abelian varieties over function fields of characteristic 0. This generalizes the recent results of Xie-Yuan, which require either the hyperbolicity assumption or the non-isotriviality assumption. The proof builds upon their strategy for constructing entire curves, yet hinges crucially on a new counting argument and draws substantially on tools from algebraic geometry and Nevanlinna theory to overcome various technical difficulties. |
| title | A counting argument for the geometric Bombieri-Lang conjecture on ramified covers of abelian varieties |
| topic | Number Theory Algebraic Geometry Complex Variables 14G05, 11G35, 11J97, 32H30 |
| url | https://arxiv.org/abs/2511.17010 |