  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 $f:{X}\rightarrow {X}$ 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 $R$.
