The Stacks project

Situation 95.15.1. Here

1. $S$ is a scheme contained in $\mathit{Sch}_{fppf}$,

2. $B$ is an algebraic space over $S$,

3. $(G, m)$ is a group algebraic space over $B$,

4. $\pi : X \to B$ is an algebraic space over $B$, and

5. $a : G \times _ B X \to X$ is an action of $G$ on $X$ over $B$.