New York Journal of Mathematics
Volume 21 (2015) 1295-1310


Jung Kyu Canci

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

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Published: December 9, 2015
Keywords: Rational functions, preperiodic points, good reduction, function fields
Subject: Primary 37P05; secondary 37P35

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.

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Universität Basel, Mathematisches Institut, Rheinsprung 21, CH-4051 Basel