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Título
Étale Covers and Fundamental Groups of Schematic Finite Spaces
Autor(es)
Materia
Schematic finite space
ringed space
finite poset
étale fundamental group
étale covers
galois category
Clasificación UNESCO
12 Matemáticas
Fecha de publicación
2022-09-09
Editor
Springer
Citación
Sánchez González, J., Tejero Prieto, C. (2022). Étale Covers and Fundamental Groups of Schematic Finite Spaces. Mediterr. J. Math. 19, 229. https://doi.org/10.1007/s00009-022-02125-z
Resumen
[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.
URI
ISSN
1660-5446
DOI
10.1007/s00009-022-02125-z
Versión del editor
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Patrocinador
Publicación en abierto financiada por el Consorcio de Bibliotecas Universitarias de Castilla y León (BUCLE), con cargo al Programa Operativo 2014ES16RFOP009 FEDER 2014-2020 DE CASTILLA Y LEÓN, Actuación:20007-CL - Apoyo Consorcio BUCLE.