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Tag 0258

Chapter 40: Étale Morphisms of Schemes > Section 40.11: Étale morphisms

Definition 40.11.1. Let $A$, $B$ be Noetherian local rings. A local homomorphism $f : A \to B$ is said to be a étale homomorphism of local rings if it is flat and an unramified homomorphism of local rings (please see Definition 40.3.1).

    The code snippet corresponding to this tag is a part of the file etale.tex and is located in lines 1048–1055 (see updates for more information).

    \begin{definition}
    \label{definition-etale-ring}
    Let $A$, $B$ be Noetherian local rings.
    A local homomorphism $f : A \to B$ is said to be a
    {\it \'etale homomorphism of local rings}
    if it is flat and an unramified homomorphism of local rings
    (please see Definition \ref{definition-unramified-rings}).
    \end{definition}

    Comments (1)

    Comment #3277 by Dario WeiƟmann on April 15, 2018 a 3:11 pm UTC

    Typo: a etale -> an etale.

    There are also 2 comments on Section 40.11: Étale Morphisms of Schemes.

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