The Lang-Vojta conjectures on projective pseudo-hyperbolic varieties

2020/02/27 by Ariyan Javanpeykar, Javanpeykar, Ariyan · 3 citations
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2002.11981

openalex publication_date 2020/02/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

These notes grew out of a mini-course given from May 13th to May 17th at UQAM in Montreal during a workshop on Diophantine Approximation and Value Distribution Theory. We start with an overview of Lang-Vojta's conjectures on pseudo-hyperbolic projective varieties. These conjectures relate various different notions of hyperbolicity. We begin with Brody hyperbolicity and discuss conjecturally related notions of hyperbolicity in arithmetic geometry and algebraic geometry in subsequent sections. We slowly work our way towards the most general version of Lang-Vojta's conjectures and provide a summary of all the conjectures, as well as a survey of recent progress.

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