nLab pro-étale morphism of schemes

Definition

A morphism of affine schemes $Spec A \to Spec B$ is pro-étale if it is a cofiltered limit of étale morphisms of schemes over $Spec B$, dually if $B \to A$ is an ind-étale algebra.

Pro étale morphisms into some scheme $X$ form the pro-étale site of $X$.

References

• Bhargav Bhatt, Peter Scholze, The pro-étale topology for schemes (arXiv:1309.1198)

Related concepts

étale morphism$\Rightarrow$ pro-étale morphism $\Rightarrow$ weakly étale morphism $\Rightarrow$ formally étale morphism