The Stacks project

Definition 78.8.2. Let $B \to S$, $G \to B$, and $X \to B$ as in Definition 78.8.1. Let $a : G \times _ B X \to X$ be an action of $G$ on $X/B$. We say the action is free if for every scheme $T$ over $B$ the action $a : G(T) \times X(T) \to X(T)$ is a free action of the group $G(T)$ on the set $X(T)$.