Some remarks on rational periodic points

Let $M$ be a finitely generated field over $\QQ$ and $X$ a variety defined over $M$. We study when the set $\{ P \in X(K) \mid f^{\circ n} (P) = P \ \text{for some} \ n \geq 1 \}$ is finite for any finite extension fields $K$ of $M$ and for any dominant $K$-morphisms $f : X \to X$ with $\deg f \geq 2$.

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Published 1 January 1999