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A Dynamical Bogomolov Property

By Lukas Pottmeyer

Abstract

A field F is said to have the Bogomolov Property related to a height function h, if h(a) is either zero or bounded from below by a positive constant for all a in F. In this paper we prove that the maximal algebraic extension of a number field K, which is unramified at a place v|p, has the Bogomolov Property related to all canonical heights coming from a Latt\`es map related to a Tate elliptic curve. To prove this algebraical statement we use analytic methods on the related Berkovich spaces

Topics: Mathematics - Number Theory, 11G50, 37P30
Year: 2011
OAI identifier: oai:arXiv.org:1103.1294
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