Lemma 33.13.1. Let $X$ be a locally Noetherian scheme over the field $k$. Let $k \subset k'$ be a finitely generated field extension. Let $x \in X$ be a point, and let $x' \in X_{k'}$ be a point lying over $x$. Then we have

If $X$ is locally of finite type over $k$, the same holds for any field extension $k \subset k'$.

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