Sur l'existence du schéma en groupes fondamentalArticleAuteurs : Marco Antei

; Michel Emsalem ; Carlo Gasbarri
0000-0001-6615-6460##NULL##NULL
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.
Comment: in French. Final version (finally!)
Volume : Volume 4
Publié le : 8 juin 2020
Accepté le : 1 avril 2020
Soumis le : 7 mai 2019
Mots-clés : Mathematics - Algebraic Geometry, Mathematics - Number Theory, 14G99, 14L15, 14L30, 11G99
Financement :
Source : OpenAIRE Graph- Foliations and algebraic geometry; Financeur: French National Research Agency (ANR); Code: ANR-16-CE40-0008
- Torsors, Vector Bundles and Fundamental Group Scheme; Financeur: French National Research Agency (ANR); Code: ANR-13-PDOC-0015