Sur l'existence du schéma en groupes fondamental

Let $S$ be a Dedekind scheme, $X$ a $S$-scheme of finite type and $x\in X(S)$ a section. We prove the existence of the fundamental group scheme of $X$ at $x$ which classifies all the finite torsors over $X$, pointed over $x$ 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 connected Galois covers in the theory of \'etale fundamental group ; we study their properties.