Definition 39.10.2. Let $S$, $G \to S$, and $X \to S$ as in Definition 39.10.1. Let $a : G \times _ S X \to X$ be an action of $G$ on $X/S$. We say the action is free if for every scheme $T$ over $S$ the action $a : G(T) \times X(T) \to X(T)$ is a free action of the group $G(T)$ on the set $X(T)$.

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