Rational functions, preperiodic points, good reduction, function fields

Subject:

Primary 37P05; secondary 37P35

Abstract

Let k be an algebraically closed field of characteristic zero. Let K be the rational function field K=k(t). Let ϕ be a nonisotrivial rational function in K(z). 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 and the degree d of ϕ.

Author information

Universität Basel, Mathematisches Institut, Rheinsprung 21, CH-4051 Basel jungkyu.canci@unibas.ch