The Stacks project

41.1 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.

Comments (2)

Comment #1485 by jojo on

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 étale 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 on

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

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View Section 41.1 as pdf