## Tag `02Z3`

Chapter 53: Algebraic Spaces > Section 53.14: Examples of algebraic spaces

Definition 53.14.4. Notation $U \to S$, $G$, $R$ as in Lemma 53.14.3. If the action of $G$ on $U$ satisfies $(*)$ we say $G$

acts freelyon the scheme $U$. In this case the algebraic space $U/R$ is denoted $U/G$ and is called thequotient of $U$ by $G$.

The code snippet corresponding to this tag is a part of the file `spaces.tex` and is located in lines 2283–2289 (see updates for more information).

```
\begin{definition}
\label{definition-quotient}
Notation $U \to S$, $G$, $R$ as in Lemma \ref{lemma-quotient}.
If the action of $G$ on $U$ satisfies $(*)$ we say $G$ {\it acts freely}
on the scheme $U$. In this case the algebraic space $U/R$ is denoted
$U/G$ and is called the {\it quotient of $U$ by $G$}.
\end{definition}
```

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