Applications of p-adic analysis for bounding periods of subvarieties\n under etale maps

2013/10/21 by Jason P. Bell, Dragos Ghioca, Bell, Jason P. +3 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.1310.5775

openalex publication_date 2013/10/21 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Using methods of p-adic analysis we give a different proof of Burnside's\nproblem for automorphisms of quasiprojective varieties X defined over a field\nof characteristic 0. More precisely, we show that any finitely generated\ntorsion subgroup of Aut(X) is finite. In particular this yields effective\nbounds for the size of torsion of any semiabelian variety over a finitely\ngenerated field of characteristic 0. More precisely, we obtain effective bounds\nfor the length of the orbit of a preperiodic subvariety under the action of an\netale map.\n

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• Preperiodic points, finiteness, and structures of semigroups of algebraic morphisms

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