On the profinite fundamental group of a connected Grothendieck topos

Fuente: arXiv
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Autori principali: Berger, Clemens, Iwaniack, Victor
Natura: Preprint
Pubblicazione: 2023
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author Berger, Clemens
Iwaniack, Victor
author_facet Berger, Clemens
Iwaniack, Victor
contents We show that finite (i.e. locally finite and decomposition-finite) objects of a connected Grothendieck topos span a Boolean pretopos with an essentially unique Galois point. The automorphism group of this point carries a profinite topology whose classifying topos is equivalent to the given Grothendieck topos if the latter is finitely generated. This leads to an intrinsic definition of the fundamental group of any connected Grothendieck topos.
format Preprint
id arxiv_https___arxiv_org_abs_2304_05338
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle On the profinite fundamental group of a connected Grothendieck topos
Berger, Clemens
Iwaniack, Victor
Category Theory
Algebraic Geometry
Primary 14G32, 18F10, Secondary 14F35, 18E50
We show that finite (i.e. locally finite and decomposition-finite) objects of a connected Grothendieck topos span a Boolean pretopos with an essentially unique Galois point. The automorphism group of this point carries a profinite topology whose classifying topos is equivalent to the given Grothendieck topos if the latter is finitely generated. This leads to an intrinsic definition of the fundamental group of any connected Grothendieck topos.
title On the profinite fundamental group of a connected Grothendieck topos
topic Category Theory
Algebraic Geometry
Primary 14G32, 18F10, Secondary 14F35, 18E50
url https://arxiv.org/abs/2304.05338