On the fundamental group scheme of rationally chain connected varieties

Abstract

Let $k$ be an algebraically closed field. Chambert-Loir proved that the étale fundamental group of a normal rationally chain connected variety over $k$ is finite. We prove that the fundamental group scheme of a normal rationally chain connected variety over $k$ is finite and étale. In particular, the fundamental group scheme of a Fano variety is finite and étale.

Final version in International Mathematics Research Notices, 2015

References in corpus (1)

• À propos du groupe fondamental des variétés rationnellement connexes