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<p>In this paper, we prove the geometric Bombieri–Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of characteristic 0. The proof is based on the idea of constructing entire curves in the presequel “Partial heights, entire curves, and the geometric Bombieri–Lang conjecture.” A new ingredient is an explicit description of the entire curves in terms of Lie algebras of abelian varieties.</p>

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The Geometric Bombieri–Lang Conjecture for Ramified Covers of Abelian Varieties

  • 期刊论文

  • 发表日期：

    2026年4月20日

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  • Junyi Xie,
  • Xinyi Yuan

摘要

In this paper, we prove the geometric Bombieri–Lang conjecture for projective varieties which have finite morphisms to abelian varieties of trivial traces over function fields of characteristic 0. The proof is based on the idea of constructing entire curves in the presequel “Partial heights, entire curves, and the geometric Bombieri–Lang conjecture.” A new ingredient is an explicit description of the entire curves in terms of Lie algebras of abelian varieties.