Strict supports of canonical measures and applications to the geometric Bogomolov conjecture

DOI10.1112/S0010437X15007721zbMath1383.14008arXiv1211.0406WikidataQ123129476 ScholiaQ123129476MaRDI QIDQ5360224

Kazuhiko Yamaki

Publication date: 28 September 2017

Published in: Compositio Mathematica (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1211.0406

zbMATH Keywords

non-Archimedean geometrygeometric Bogomolov conjecturecanonical measures

Mathematics Subject Classification ID

Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Subvarieties of abelian varieties (14K12) Rigid analytic geometry (14G22)

Related Items

Non-density of small points on divisors on Abelian varieties and the Bogomolov conjecture, Geometric Bogomolov conjecture in arbitrary characteristics, Trace of abelian varieties over function fields and the geometric Bogomolov conjecture, On Zhang's semipositive metrics, Effective faithful tropicalizations associated to linear systems on curves

Cites Work

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• Geometric Bogomolov conjecture for abelian varieties and some results for those with some degeneration (with an appendix by Walter Gubler: the minimal dimension of a canonical measure)
• Admissible pairing on a curve
• Equidistribution over function fields
• Effective calculation of the geometric height and the Bogomolov conjecture for hyperelliptic curves over function fields
• Equidistribution of small points on abelian varieties
• Positivity and discretion of algebraic points of curves
• Degenerating abelian varieties
• Rigid analytische Gruppen mit guter Reduktion
• Smooth \(p\)-adic analytic spaces are locally contractible
• Vanishing cycles for formal schemes
• Étale cohomology for non-Archimedean analytic spaces
• Smoothness, semi-stability and alterations
• Equidistribution of small points
• Bogomolov conjecture for curves of genus 2 over function fields
• Geometric Bogomolov's conjecture for curves of genus 3 over function fields.
• Arithmetic height functions over finitely generated fields
• Tropical varieties for non-archimedean analytic spaces
• The Bogomolov conjecture for totally degenerate abelian varieties
• Zhang's conjecture and the effective Bogomolov conjecture over function fields
• Bogomolov conjecture over function fields for stable curves with only irreducible fibers (Version 2.0)
• A positive characteristic Manin–Mumford theorem
• The Geometric Bogomolov Conjecture for Curves of Small Genus
• Non-archimedean canonical measures on abelian varieties
• Néron Models
• Relative Bogomolov’s inequality and the cone of positive divisors on the moduli space of stable curves
• Mesures et équidistribution sur les espaces de Berkovich