Lemma 78.6.3. Let $S$ be a scheme. Let $B$ be an algebraic space over $S$. Let $G$ be a group algebraic space over $B$. Assume $G \to B$ is locally of finite type.

There exists a maximal open subspace $U \subset B$ such that $G_ U \to U$ is unramified and formation of $U$ commutes with base change.

There exists a maximal open subspace $U \subset B$ such that $G_ U \to U$ is locally quasi-finite and formation of $U$ commutes with base change.

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