The Stacks project

Lemma 33.10.5. Let $k$ be a field. Let $X$ be a geometrically normal scheme over $k$ and let $Y$ be a normal scheme over $k$. Then $X \times _ k Y$ is a normal scheme.

Proof. This reduces to Algebra, Lemma 10.165.5 by Lemma 33.10.3. $\square$

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