Lemma 77.9.5. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $G$ be a group algebraic space over $B$. Let $X$ be a pseudo $G$-torsor over $B$. Assume $G$ and $X$ locally of finite type over $B$.

If $G \to B$ is unramified, then $X \to B$ is unramified.

If $G \to B$ is locally quasi-finite, then $X \to B$ is locally quasi-finite.

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