Étale Covers and Fundamental Groups of Schematic Finite Spaces
[EN] We introduce the category of finite étale covers of an arbitraryschematic space X and show that, equipped with an appropriate naturalfiber functor, it is a Galois Category. This allows us to define the étale fundamental group of schematic spaces. If X is a finite model of a schemeS, we show tha...
| Autores: | , |
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| Formato: | artículo |
| Estado: | Versión publicada |
| Fecha de publicación: | 2022 |
| País: | España |
| Recursos: | Universidad de Salamanca (USAL) |
| Repositorio: | GREDOS. Repositorio Institucional de la Universidad de Salamanca |
| OAI Identifier: | oai:gredos.usal.es:10366/150983 |
| Acesso em linha: | http://hdl.handle.net/10366/150983 |
| Access Level: | acceso abierto |
| Palavra-chave: | Schematic finite space ringed space finite poset étale fundamental group étale covers galois category 12 Matemáticas |
| Resumo: | [EN] We introduce the category of finite étale covers of an arbitraryschematic space X and show that, equipped with an appropriate naturalfiber functor, it is a Galois Category. This allows us to define the étale fundamental group of schematic spaces. If X is a finite model of a schemeS, we show that the resulting Galois theory on X coincides with theclassical theory of finite étale covers on S, and therefore, we recover the classical étale fundamental group introduced by Grothendieck. Toprove these results, it is crucial to find a suitable geometric notion ofconnectedness for schematic spaces and also to study their geometric points. We achieve these goals by means of the strong cohomologicalconstraints enjoyed by schematic spaces. |
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