Lemma 105.14.3. Let $p : \mathcal{X} \to Y$ be a morphism from an algebraic stack to an algebraic space. Assume

$\mathcal{I}_\mathcal {X} \to \mathcal{X}$ is finite,

$p$ is proper, and

$Y$ is locally Noetherian.

Let $f : \mathcal{X} \to M$ be the moduli space constructed in Theorem 105.13.9. Then $M \to Y$ is proper.

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