Partial heights, entire curves, and the geometric Bombieri-Lang conjecture
Abstract
We introduce a new approach to the geometric Bombieri-Lang conjecture for hyperbolic varieties in characteristic zero. The main idea is to construct an entire curve on a special fiber of a variety over a complex function field from an infinite sequence of rational points of the variety. The construction relies on the classical Brody lemma in complex geometry and is conditional on a non-degeneracy conjecture of partial heights. In particular, we prove the geometric Bombieri-Lang conjecture for hyperbolic projective varieties which have finite morphisms to abelian varieties over function fields of characteristic zero.
Fields of Study & Subjects
Algebraic Geometry and Number Theory
Meromorphic and Entire Functions
Advanced Differential Equations and Dynamical Systems
Publication details
- Journal / source
- Acta Mathematica
- Publisher
- International Press of Boston
- Volume
- 236
- Issue
- 2
- Pages
- 365–416
- Publication date
- 1 January 2026
- Language
- EN