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

Canci, Jung Kyu and Paladino, Laura. (2015) Preperiodic points for rational functions defined over a global field in terms of good reduction. Preprints Fachbereich Mathematik, 2015 (37).

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Official URL: https://edoc.unibas.ch/70002/

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 $\phi$ in terms of the number of places of bad reduction. The result is completely new in the function field case and it is an improvement of the number field case.