Geometric Bogomolov conjecture for semiabelian varieties

2025/05/12 by Wenbin Luo, Luo, Wenbin, Jiawei Yu +1
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT) #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.2505.07193

openalex publication_date 2025/05/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We establish the geometric Bogomolov conjecture for semiabelian varieties over function fields. We show a closed subvariety contains Zariski dense sets of small points, if and only if, after modulo its stabilizer, it is a torsion translate of a constant variety. A new phenomenon is that a special subvariety may not have a Zariski dense set of points of height 0.

Citations

• Chow trace of 1-motives and the Lang-Néron groups
• Arakelov geometry over adelic curves
• Points of Small Height on Semiabelian Varieties
• Heights in families of abelian varieties and the Geometric Bogomolov Conjecture
• Some structure theorems for algebraic groups
• Mordell-Lang in positive characteristic
• The arithmetic Hodge index theorem for adelic line bundles I
• Zhang's Conjecture and the Effective Bogomolov Conjecture over function fields
• On Hrushovski's proof of the Manin-Mumford conjecture
• Points de petite hauteur sur les varietes semi-abeliennes
• Arithmetic height functions over finitely generated fields
• Positivite et discretion des points algebriques des courbes
• Hodge index theorem for arithmetic cycles of codimension one

Related

• Survey on the geometric Bogomolov conjecture
• Points of small height on varieties defined over a function field
• Points de petite hauteur sur les varietes semi-abeliennes
• Bogomolov conjecture for curves of genus 2 over function fields
• Points of Small Height on Semiabelian Varieties