Geometric and arithmetic subgroups of the Grothendieck-Teichmüller group.
type: Item
instance of: scholarly article
title: Geometric and arithmetic subgroups of the Grothendieck-Teichmüller group.
zbMATH Open document ID: 1052.14025
author: Hidekazu Furusho
published in: Mathematical Research Letters
publication date: 2004-03-08T00:00:00Z
review text: The Grothendieck-Teichmüller group \(\widehat{GT}\) is a subgroup of the automorphism group \(\Aut\widehat F_2\) of the free profinite group \(\widehat F_2\) of rank 2. \textit{Y. Ihara} [in: The Grothendieck theory of dessins d'enfants. Lond. Math. Soc. Lect. Note Ser. 200, 289--321 (1994; Zbl 0849.12005)] showed that the absolute Galois group \(\text{Gal}(\overline{\mathbb Q}/{\mathbb Q})\) can be embedded in \(\widehat{GT}\). It is still open whether \(\text{Gal} (\overline{\mathbb Q}/{\mathbb Q})\) is equal to \(\widehat{GT}\). In this article the author studies connections between several new-type relations satisfied by \(\text{Gal} (\overline{\mathbb Q}/{\mathbb Q})\) and \(\widehat{GT}\) that were discovered recently.
Mathematics Subject Classification ID: 14G32
Mathematics Subject Classification ID: 20E18
zbMATH DE Number: 1918965
zbMATH Keywords: profinite groups
zbMATH Keywords: absolute Galois group
reviewed by: Pavel Zalesskij
MaRDI profile type: Publication
full work available at URL: mrl.2003.v10.n1.a10
OpenAlex ID: W2059711478
DOI: 10.4310/MRL.2003.V10.N1.A10
description: scientific article; zbMATH DE number 1918965