Fundamental groups of proper varieties are finitely presented

Abstract

It was recently proven by Esnault, Shusterman and the second named author, that the étale fundamental group of a connected smooth projective variety over an algebraically closed field $k$ is finitely presented. In this note, we extend this result to all connected proper schemes over $k$.

Final version, accepted for publication in Comptes Rendus Mathématique, https://comptes-rendus.academie-sciences.fr/mathematique. Besides various minor improvements, a new section "More general base fields" was added