Sur l'existence du schéma en groupes fondamental

Abstract

Let $S$ be a Dedekind scheme, $X$ a connected $S$-scheme locally of finite type and $x\in X(S)$ a section. The aim of the present paper is to establish the existence of the fundamental group scheme of $X$, when $X$ has reduced fibers or when $X$ is normal. We also prove the existence of a group scheme, that we will call the quasi-finite fundamental group scheme of $X$ at $x$, which classifies all the quasi-finite torsors over $X$, pointed over $x$. We define Galois torsors, which play in this context a role similar to the one of Galois covers in the theory of étale fundamental group.

in French. Final version (finally!)

References in corpus (1)

• Tannakian duality over Dedekind rings and applications

Cited by in corpus (2)

• Extension of torsors and prime to $p$ fundamental group scheme
• The pseudo-fundamental group-scheme