A Dynamical Bogomolov Property
Number Theory
2011-03-08 v1
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.
Keywords
Cite
@article{arxiv.1103.1294,
title = {A Dynamical Bogomolov Property},
author = {Lukas Pottmeyer},
journal= {arXiv preprint arXiv:1103.1294},
year = {2011}
}