Sur l'existence du schéma en groupes fondamentalArticle
Auteurs : 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.
Torsors, Vector Bundles and Fundamental Group Scheme; Financeur: French National Research Agency (ANR); Code: ANR-13-PDOC-0015
Foliations and algebraic geometry; Financeur: French National Research Agency (ANR); Code: ANR-16-CE40-0008
Références bibliographiques
2 Documents citant cet article
Marco Antei;Jimmy Calvo-Monge, 2022, Extension of torsors and prime to p fundamental group scheme, Annales de l’institut Fourier, 72, 1, pp. 367-386, 10.5802/aif.3475, https://doi.org/10.5802/aif.3475.
Marco Antei;Michel Emsalem;Carlo Gasbarri, 2020, Erratum for “Heights of vector bundles and the fundamental group scheme of a curve”, Duke Mathematical Journal, 169, 16, 10.1215/00127094-2020-0065.