English

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}
}
R2 v1 2026-06-21T17:36:05.303Z