Étale Covers and Fundamental Groups of Schematic Finite Spaces

Autor: J. Sánchez González, C. Tejero Prieto
Rok vydání: 2022
Předmět:
Zdroj: GREDOS. Repositorio Institucional de la Universidad de Salamanca
instname
ISSN: 1660-5454
1660-5446
DOI: 10.1007/s00009-022-02125-z
Popis: [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.
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.
Databáze: OpenAIRE
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