# The Stacks Project

## Tag 07S1

Definition 38.10.2. Let $S$, $G \to S$, and $X \to S$ as in Definition 38.10.1. 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 $X(T)$.

The code snippet corresponding to this tag is a part of the file groupoids.tex and is located in lines 1983–1991 (see updates for more information).

\begin{definition}
\label{definition-free-action}
Let $S$, $G \to S$, and $X \to S$ as in
Definition \ref{definition-action-group-scheme}.
Let $a : G \times_S X \to X$ be an action of $G$ on $X/S$.
We say the action is {\it 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 $X(T)$.
\end{definition}

There are no comments yet for this tag.

## Add a comment on tag 07S1

In your comment you can use Markdown and LaTeX style mathematics (enclose it like $\pi$). A preview option is available if you wish to see how it works out (just click on the eye in the lower-right corner).