Uniform Bounds for Periods of Endomorphisms of Varieties

Abstract

Suppose $X$ is a projective variety defined over a finite extension $K$ of ${\mathbb{Q}}_p$ and suppose $X$ admits a model $\mathcal{X}$ defined over the ring of integers $R$ of $K$. Let $f:X\to X$ be an endomorphism of $X$ defined over $K$ that can be extended to an endomorphism of $\mathcal{X}$ defined over $R$. We apply a method of Fakhruddin to prove an explicit upper bound for the primitive period of periodic points defined over $R$.

8 pages