The Stacks Project


Tag 024K

40.1. Introduction

In this Chapter, we discuss étale morphisms of schemes. We illustrate some of the more important concepts by working with the Noetherian case. Our principal goal is to collect for the reader enough commutative algebra results to start reading a treatise on étale cohomology. An auxiliary goal is to provide enough evidence to ensure that the reader stops calling the phrase ''the étale topology of schemes'' an exercise in general nonsense, if (s)he does indulge in such blasphemy.

We will refer to the other chapters of the Stacks project for standard results in algebraic geometry (on schemes and commutative algebra). We will provide detailed proofs of the new results that we state here.

    The code snippet corresponding to this tag is a part of the file etale.tex and is located in lines 18–38 (see updates for more information).

    \section{Introduction}
    \label{section-introduction}
    
    \noindent
    In this Chapter, we discuss \'etale morphisms of schemes. We illustrate
    some of the more important concepts by working with the Noetherian case.
    Our principal goal is to collect for the reader enough commutative
    algebra results to start reading a treatise on \'etale cohomology. An
    auxiliary goal is to provide enough evidence to ensure that the reader stops
    calling the phrase ``the \'etale topology of schemes'' an exercise in general
    nonsense, if (s)he does indulge in such blasphemy.
    
    \medskip\noindent
    We will refer to the other
    chapters of the Stacks project for standard results in algebraic geometry
    (on schemes and commutative algebra). We will provide detailed
    proofs of the new results that we state here.

    Comments (2)

    Comment #1485 by jojo on June 6, 2015 a 9:15 am UTC

    There is something weird with this sentence :

    "Our principal goal is to collect for the reader with enough commutative algebra results to start reading a treatise on ├ętale cohomology"

    English isn't my first language so I might be wrong but I feel like it's missing a comma or a few words (or both ?).

    Comment #1499 by Johan (site) on June 7, 2015 a 1:05 pm UTC

    My first language is dutch... Anyway by removing one word it seems the sentence works better. See here.

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