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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