# The Stacks Project

## Tag: 04RV

This tag has label spaces-more-groupoids-situation-etale-localize-quasi and it points to

The corresponding content:

Situation 57.11.3. (Assumptions for quasi-splitting.) Let $S$ be a scheme. Let $(U, R, s, t, c)$ be a groupoid scheme over $S$. Let $u \in U$ be a point. Assume that
1. $s, t : R \to U$ are separated,
2. $s$, $t$ are locally of finite type, and
3. $s$ is quasi-finite at $e(u)$.

\begin{situation}
\label{situation-etale-localize-quasi}
(Assumptions for quasi-splitting.)
Let $S$ be a scheme.
Let $(U, R, s, t, c)$ be a groupoid scheme over $S$.
Let $u \in U$ be a point. Assume that
\begin{enumerate}
\item $s, t : R \to U$ are separated,
\item $s$, $t$ are locally of finite type, and
\item $s$ is quasi-finite at $e(u)$.
\end{enumerate}
\end{situation}

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