Simple connectivity of Fargues–Fontaine curves

Kedlaya, Kiran S.

doi:10.5802/ahl.101

Kedlaya, Kiran S.

Simple connectivity of Fargues–Fontaine curves

Annales Henri Lebesgue, Volume 4 (2021), pp. 1203-1233.

Metadata

DOI10.5802/ahl.101

Keywords perfectoid spaces, Fargues–Fontaine curves, Drinfeld’s lemma

Abstract

We show that the Fargues–Fontaine curve associated to an algebraically closed field of characteristic $p$ is geometrically simply connected; that is, its base extension from $ℚ_{p}$ to any complete algebraically closed overfield admits no nontrivial connected finite étale covering. We then deduce from this an analogue for perfectoid spaces (and some related objects) of Drinfeld’s lemma on the fundamental group of a product of schemes in characteristic $p$ .

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