Preperiodic points for rational functions defined over a global field in terms of good reduction

Let $phi$ be an endomorphism of the projective line defined over a global field $K.$ We prove a bound for the cardinality of the set of $K$–rational preperiodic points for φ in terms of the number of places of bad reduction. The result is completely new in the function field case and is an improvement of the number field case.

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