nLab w-contractible ring

Contents

Definition

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

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

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

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

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