An Effective Dynamical Bogomolov Property

Details An Effective Dynamical Bogomolov Property An Effective Dynamical Bogomolov Property

2012-01-16

arxiv.org/abs/1201.3327v1

Mathematics

Number Theory

Scientific paper

Let E be an Tate elliptic curve defined over a number field K with fixed non-archimedean absolute value v and let f be an associated Latt\`es map. In a previous paper we proved that the maximal algebraic extension of K, which is unramified at v, has the Bogomolov-Property related to the canonical height related to f (i.e. the height is either 0 or bounded from below by a positive constant). In this paper we make this bound effective and generalize the previous result to sets with bounded ramification indices over v. We also prove that an analogue result for the N\'eron-Tate height on E is true.

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