Authors: Marco Antei ; Michel Emsalem ; Carlo Gasbarri
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Marco Antei;Michel Emsalem;Carlo Gasbarri
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.
Antei, Marco; Emsalem, Michel; Gasbarri, Carlo, 2020, Erratum For âHeights Of Vector Bundles And The Fundamental Group Scheme Of A Curveâ, Duke Mathematical Journal, 169, 16, 10.1215/00127094-2020-0065.