Existence of non-preperiodic algebraic points for a rational self-map of infinite order

Details Existence of non-preperiodic algebraic points for a rational self-map of infinite order Existence of non-preperiodic algebraic points for a rational self-map of infinite order

2010-07-09

arxiv.org/abs/1007.1635v1

Mathematics

Algebraic Geometry

6 pages, LaTeX

Scientific paper

Let $X$ be a variety defined over a number field and $f$ be a dominant rational self-map of $X$ of infinite order. We show that $X$ admits many algebraic points which are not preperiodic under $f$. If $f$ were regular and polarized, this would follow immediately from the theory of canonical heights, but it does not work very well for rational self-maps. We provide an elementary proof following an argument by Bell, Ghioca and Tucker (arxiv:0808.3266).

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