Simple connectivity of Fargues–Fontaine curves
Annales Henri Lebesgue, Volume 4 (2021), pp. 1203-1233.

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 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.

On montre que la courbe de Fargues–Fontaine associée à un corps algébriquement clos de caractéristique p est géométriquement simplement connexe ; c’est-à-dire que son extension de base de p à tout corps complet algébriquement clos n’admet aucun revêtement étale connexe non trivial. On en déduit alors un analogue pour les espaces perfectoïdes (et certains objets associés) du lemme de Drinfeld sur le groupe fondamental d’un produit de schémas en caractéristique p.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/ahl.101
Classification: 14G45, 14F35
Keywords: perfectoid spaces, Fargues–Fontaine curves, Drinfeld’s lemma
Kedlaya, Kiran S. 1

1 Department of Mathematics, University of California San Diego, 9500 Gilman Drive #0112, La Jolla, CA 92093, (USA)
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Kedlaya, Kiran S. Simple connectivity of Fargues–Fontaine curves. Annales Henri Lebesgue, Volume 4 (2021), pp. 1203-1233. doi : 10.5802/ahl.101. http://archive.numdam.org/articles/10.5802/ahl.101/

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