Parshin's method and the geometric Bombieri-Lang conjecture

2024/07/15 by Finn Bartsch, Bartsch, Finn, Ariyan Javanpeykar +1 · 1 citation
Engineering · Mathematics · #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2407.10706

openalex publication_date 2024/07/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this short survey, we explain Parshin's proof of the geometric Bombieri-Lang conjecture, and show that it can be used to give an alternative proof of Xie-Yuan's recent resolution of the geometric Bombieri-Lang conjecture for projective varieties with empty special locus and admitting a finite morphism to a traceless abelian variety.

Cited by

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

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