The Stacks project

Lemma 71.4.3. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. If $f$ is locally of finite type, then the fibres of $f$ are locally Noetherian.

Proof. This follows from Morphisms of Spaces, Lemma 67.23.5 and the fact that the spectrum of a field is Noetherian. $\square$

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