Lemma 38.9.3. Let $R$ be a ring. Let $R \to S$ be a ring map. Assume
$R \to S$ is of finite presentation and flat, and
every fibre ring $S \otimes _ R \kappa (\mathfrak p)$ is geometrically integral over $\kappa (\mathfrak p)$.
Then $S$ is projective as an $R$-module.