Sur l'existence du schéma en groupes fondamental
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2015
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| _version_ | 1866916197937709056 |
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| author | Antei, Marco Emsalem, Michel Gasbarri, Carlo |
| author_facet | Antei, Marco Emsalem, Michel Gasbarri, Carlo |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1504_05082 |
| institution | arXiv |
| publishDate | 2015 |
| record_format | arxiv |
| spellingShingle | Sur l'existence du schéma en groupes fondamental Antei, Marco Emsalem, Michel Gasbarri, Carlo Algebraic Geometry Number Theory 14G99, 14L15, 14L30, 11G99 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. |
| title | Sur l'existence du schéma en groupes fondamental |
| topic | Algebraic Geometry Number Theory 14G99, 14L15, 14L30, 11G99 |
| url | https://arxiv.org/abs/1504.05082 |