Definition 71.4.2. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $y \in |Y|$. We say the fibre of $f$ over $y$ is locally Noetherian if the equivalent conditions (1), (2), and (3) of Lemma 71.4.1 are satisfied. We say the fibres of $f$ are locally Noetherian if this holds for every $y \in |Y|$.
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