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arXiv · 2511.17010

A counting argument for the geometric Bombieri-Lang conjecture on ramified covers of abelian varieties

Guoquan Gao
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Abstract

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.

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Guoquan Gao. 2026-03-02. A counting argument for the geometric Bombieri-Lang conjecture on ramified covers of abelian varieties. https://arxiv.org/abs/2511.17010

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