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The Stacks project

Proposition 99.9.4. Let S be a scheme. Let f : X \to B be a morphism of algebraic spaces over S. If f is of finite presentation and separated, then \mathrm{Hilb}_{X/B} is an algebraic space locally of finite presentation over B.

Proof. Immediate consequence of Lemma 99.9.2 and Proposition 99.8.4. \square


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