A remark on the moduli field of a curve
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.
scientific article; zbMATH DE number 2051571