A remark on the moduli field of a curve
type: Item
instance of: scholarly article
title: A remark on the moduli field of a curve
zbMATH Open document ID: 1048.14013
author: Horst Hammer
author: Frank Herrlich
published in: Archiv der Mathematik
publication date: 2004-03-07T00:00:00Z
review text: A nonsingular projective variety \(X\) over an algebraically closed field \(C\) defines two subfields, the field of definition \(D(X)\) and the moduli field \(M(X)\), such that \(M(X)\subseteq D(X)\subset C\). According to \textit{J. Wolfart} [ Schneps, Leila (ed.) et al., Geometric Galois actions. 1. Around Grothendieck's ``Esquisse d'un programme''. Proceedings of the conference on geometry and arithmetic of moduli spaces, Luminy, France, August 1995. Cambridge: Cambridge University Press. Lond. Math. Soc. Lect. Note Ser. 242, 97--112 (1997; Zbl 0915.14021)], for curves \(X\) in characteristic 0, the field of definition \(D(X)\) can be chosen as a finite algebraic extension of \(M(X)\). In the paper presents a purely algebro-geometric version of Wolfart's proof, extended to curves over algebraically closed fields of arbitrary characteristic.
Mathematics Subject Classification ID: 14H25
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 11G30
zbMATH DE Number: 2051571
zbMATH Keywords: algebraic curves
zbMATH Keywords: field of definition
zbMATH Keywords: moduli field
reviewed by: Christina Birkenhake
MaRDI profile type: Publication
full work available at URL: s00013-003-4649-5
OpenAlex ID: W2037877587
DOI: 10.1007/S00013-003-4649-5
description: scientific article; zbMATH DE number 2051571