# Contents

## Definition

###### Definition

A commutative ring $R$ is w-contractible if every faithfully flat pro-étale morphism $Spec A \to Spec R$ has a section.

## Properties

###### Proposition

For every commutative ring $R$, there is a w-contractible $A$, def. , equipped with a faithfully flat pro-étale morphism $Spec A \to Spec R$.

###### Proposition

For $R$ w-contractible, the profinite set $\pi_0(Spec R)$ is an extremally disconnected profinite set.

part of (Bhatt-Scholze 13, theorem 1.8)

## References

Last revised on November 21, 2013 at 09:38:30. See the history of this page for a list of all contributions to it.