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arXiv · 1103.1294

A Dynamical Bogomolov Property

Lukas Pottmeyer
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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 Lattès map related to a Tate elliptic curve. To prove this algebraical statement we use analytic methods on the related Berkovich spaces.

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Lukas Pottmeyer. 2011-03-07. A Dynamical Bogomolov Property. https://arxiv.org/abs/1103.1294

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