Coupling of universal monodromy representations of Galois-Teichmüller modular groups
type: Item
instance of: scholarly article
title: Coupling of universal monodromy representations of Galois-Teichmüller modular groups
zbMATH Open document ID: 0835.14007
DOI: 10.1007/BF01446287
published in: Mathematische Annalen
publication date: 1996-04-15T00:00:00Z
full work available at URL: https://eudml.org/doc/165397
review text: Let \(M_{g,n}\) be the moduli stack of smooth projective curves of genus \(g\) with \(n\)-marked points, and let \(l\) be a rational prime. The pro-\(l\) universal monodromy representations of Galois-Teichmüller modular groups define canonical pro-\(l\) towers \(\{\mathbb{Q}_{g,n} (m)\}^\infty_{m = 1}\) of fields of definition of certain natural profinite coverings of \(M_{g,n}\). These field towers are shown to be independent of \(n \geq 1\) in a previous paper by \textit{H. Nakamura}, \textit{N. Takao} and \textit{R. Ueno} [Math. Ann. 302, No. 2, 197-213 (1955; Zbl 0826.14016)] and in this paper a fundamental relation with respect to genera: \(\mathbb{Q}_{0,3} (m) \subset \mathbb{Q}_{g,n} (m) \subset \mathbb{Q}_{1,1} (m)\) \((n \geq 1)\) is established. This result leads to applications to certain nonabelian analogs of the Tate conjecture and to a topological problem of estimation of the Johnson homomorphisms.
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 11F55
zbMATH DE Number: 840216
zbMATH Keywords: projective curves of genus \(g\) with \(n\)-marked points
zbMATH Keywords: pro-\(l\) towers of fields of definition
zbMATH Keywords: moduli stack
zbMATH Keywords: Galois-Teichmüller modular groups
zbMATH Keywords: nonabelian analogs of the Tate conjecture
author: Hiroaki Nakamura
MaRDI profile type: Publication
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OpenAlex ID: W2053410225
description: scientific article; zbMATH DE number 840216