Lemma 71.2.8. Let S be a scheme. Let X be a locally Noetherian algebraic space over S. Let \mathcal{F} be a coherent \mathcal{O}_ X-module. Then \text{Ass}(\mathcal{F}) \cap W is finite for every quasi-compact open W \subset |X|.
Proof. Choose a quasi-compact scheme U and an étale morphism U \to X such that W is the image of |U| \to |X|. Then U is a Noetherian scheme and we may apply Divisors, Lemma 31.2.5 to conclude. \square
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