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.

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