Corollary 3

Tag 0D1T, permanent. Cite it as [Bourbaki, Tag 0D1T].

Commutative Algebra, chapter X, § 1. Profondeur

Let $\rho : A \to B$ be a homomorphism of noetherian rings. Assume that $B$ is a flat $A$ -module, that $A$ is normal, and that $\kappa(p) \otimes_A B$ is normal for every $p \in \mathrm{Spec}(A)$ . Then $B$ is normal.

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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