Seminar Algebra and Geometry: Jung Kyu Canci (Universität Basel)

Preperiodic points over global fields

I will present a joint work with Laura Paladino.

We consider dynamical systems on the projective line given by rational functions. 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 fields case and it is an improvement of the number fields case. An important tool is an S-unit equation theorem in 2 variables.

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