Lemma 38.31.2. Let $S$ be a quasi-compact and quasi-separated scheme. Let $X$ be a scheme over $S$. Let $U \subset S$ be a quasi-compact open. Assume
$X \to S$ is proper, and
$X_ U \to U$ is finite locally free.
Then there exists a $U$-admissible blowup $S' \to S$ such that the strict transform of $X$ is finite locally free over $S'$.