Let $k$ be an algebraic closed field of characteristic zero. Let $K$ be the
rational function field $K=k(t)$. Let $\phi$ be a non isotrivial rational
function in $K(z)$. 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 and the degree $d$ of $\phi$.Comment: There was a mistake in the previous version. The results have been
  proven only for rational function field

Canci, J. K.

English

arXiv

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

Canci, Jung Kyu

edoc

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

Let k be an algebraic closed field of characteristic zero. Let K be the rational function field K = k(t). Let $\phi$  be a non–isotrivial rational function in K(z). 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 and the degree d of $\phi$

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

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

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