nLab
w-contractible ring

Context

Geometry

Étale morphisms

Contents

Definition

Definition

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

(Bhatt-Scholze 13, def. 2.4.1)

Properties

Proposition

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

(Bhatt-Scholze 13, lemma 2.4.9)

Proposition

For RR w-contractible, the profinite set π 0(SpecR)\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.