Equidistribution over function fields

DOI10.1007/s00229-008-0198-3zbMath1189.14030arXiv0801.4508OpenAlexW2163841091MaRDI QIDQ1003139

Walter Gubler

Publication date: 26 February 2009

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

Full work available at URL: https://arxiv.org/abs/0801.4508

zbMATH Keywords

function fieldsalgebraic varietiesconvex geometrytropical varietiessmall pointsequidistribution measuresfundamental inequality

Mathematics Subject Classification ID

Related Items (19)

Non-density of small points on divisors on Abelian varieties and the Bogomolov conjecture ⋮ Points of small height on semiabelian varieties ⋮ Geometric Bogomolov conjecture in arbitrary characteristics ⋮ Trace of abelian varieties over function fields and the geometric Bogomolov conjecture ⋮ Greatest common divisors of iterates of polynomials ⋮ Quantitative equidistribution of Galois orbits of small points in the \(N\)-dimensional torus ⋮ 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) ⋮ Higher dimensional essential minima and equidistribution of cycles ⋮ Height coincidences in products of the projective line ⋮ Strict supports of canonical measures and applications to the geometric Bogomolov conjecture ⋮ Global pluripotential theory over a trivially valued field ⋮ Equidistribution of preimages over nonarchimedean fields for maps of good reduction ⋮ On Zhang's semipositive metrics ⋮ Finite index theorems for iterated Galois groups of cubic polynomials ⋮ The dynamical Manin–Mumford conjecture and the dynamical Bogomolov conjecture for endomorphisms of ⋮ A criterion for weak convergence on Berkovich projective space ⋮ Approches courantielles à la Mellin dans un cadre non archimédien ⋮ Successive minima and asymptotic slopes in Arakelov geometry ⋮ Solution to a non-Archimedean Monge-Ampère equation

Cites Work

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• Equidistribution of small points on abelian varieties
• Positivity and discretion of algebraic points of curves
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• The direct image theorem in formal and rigid geometry
• Equidistribution of small points
• Limit distribution of small points on algebraic tori
• Equidistribution of small subvarieties of an Abelian variety
• Tropical varieties for non-archimedean analytic spaces
• The Bogomolov conjecture for totally degenerate abelian varieties
• Equidistribution of subvarieties of small height
• Local heights of subvarieties over non-archimedean fields
• Mesures et équidistribution sur les espaces de Berkovich

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