The Stacks project

Proposition 97.11.5. Let $S$ be a scheme. Let $X \to Z \to B$ be morphisms of algebraic spaces over $S$. If $Z \to B$ is finite locally free then $\text{Res}_{Z/B}(X)$ is an algebraic space.

Proof. By Proposition 97.10.4 the functors $\mathit{Mor}_ B(Z, X)$ and $\mathit{Mor}_ B(Z, Z)$ are algebraic spaces. Hence this follows from the cartesian diagram of Lemma 97.11.4 and the fact that fibre products of algebraic spaces exist and are given by the fibre product in the underlying category of sheaves of sets (see Spaces, Lemma 65.7.2). $\square$

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