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Tag 04RH

Chapter 55: Morphisms of Algebraic Spaces > Section 55.38: Étale morphisms

Definition 55.38.1. Let $S$ be a scheme. Let $f : X \to Y$ be a morphism of algebraic spaces over $S$. Let $x \in |X|$. We say $f$ is étale at $x$ if there exists an open neighbourhood $X' \subset X$ of $x$ such that $f|_{X'} : X' \to Y$ is étale.

    The code snippet corresponding to this tag is a part of the file spaces-morphisms.tex and is located in lines 7537–7544 (see updates for more information).

    \begin{definition}
    \label{definition-etale}
    Let $S$ be a scheme.
    Let $f : X \to Y$ be a morphism of algebraic spaces over $S$.
    Let $x \in |X|$. We say $f$ is {\it \'etale at $x$} if there
    exists an open neighbourhood $X' \subset X$ of $x$ such that
    $f|_{X'} : X' \to Y$ is \'etale.
    \end{definition}

    Comments (2)

    Comment #2456 by Matthieu Romagny on March 15, 2017 a 12:56 pm UTC

    Final point missing.

    Comment #2495 by Johan (site) on April 13, 2017 a 11:15 pm UTC

    Thanks, fixed here.

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