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Tag 02Z3

Chapter 56: Algebraic Spaces > Section 56.14: Examples of algebraic spaces

Definition 56.14.4. Notation $U \to S$, $G$, $R$ as in Lemma 56.14.3. If the action of $G$ on $U$ satisfies $(*)$ we say $G$ acts freely on the scheme $U$. In this case the algebraic space $U/R$ is denoted $U/G$ and is called the quotient 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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