The Stacks project

Lemma 97.14.1. Let $S$ be a scheme. Let $X$ be an algebraic space over $S$. Then $\mathcal{H}_ d(X)$ is an algebraic stack.

Proof. The $1$-morphism

\[ \mathcal{H}_ d(X) \longrightarrow \mathcal{H}_ d \]

is representable by algebraic spaces according to Lemma 97.12.6. The stack $\mathcal{H}_ d$ is an algebraic stack according to Proposition 97.13.2. Hence $\mathcal{H}_ d(X)$ is an algebraic stack by Algebraic Stacks, Lemma 94.15.4. $\square$

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