Preperiodic points for rational functions defined over a rational function field of characteristic zero

Abstract

Let $k$ be an algebraic closed field of characteristic zero. Let $K$ be the rational function field $K=k(t)$. Let $\varphi$ be a non isotrivial rational function in $K(z)$. We prove a bound for the cardinality of the set of $K$--rational preperiodic points for $\varphi$ in terms of the number of places of bad reduction and the degree $d$ of $\varphi$.

There was a mistake in the previous version. The results have been proven only for rational function fields

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