Ramified primes in the field of moduli of branched coverings of curves
type: Item
instance of: scholarly article
title: Ramified primes in the field of moduli of branched coverings of curves
zbMATH Open document ID: 0698.14024
DOI: 10.1016/0021-8693(89)90303-7
author: Sybilla Beckmann
published in: Journal of Algebra
publication date: 1989-01-01T00:00:00Z
review text: Let \({\mathcal D}\) be an algebraic curve over \({\mathbb{C}}\) which is also defined over a number field F. Let G be a finite group and let \({\mathcal C}\to {\mathcal D}\) be a G-galois branched covering of \({\mathcal D}\) whose branch points are defined over a finite extension of F. The main result is that the set of finite primes of F which ramify in the field of moduli of the covering (the fixed field of those automorphisms of \(\bar F\) over F which preserve the covering and its G-action) is contained in the union of the set of primes of bad reduction of \({\mathcal D}\), the set of primes dividing the order of G and the set of primes p for which the branch locus becomes singular modulo p. The proof proceeds by first examining the primes of bad reduction of the branched covering.
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14H10
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14H25
zbMATH DE Number: 4144133
zbMATH Keywords: field of definition
zbMATH Keywords: galois branched covering
zbMATH Keywords: field of moduli of the covering
zbMATH Keywords: bad reduction
MaRDI profile type: Publication
full work available at URL: 0021-8693(89)90303-7
OpenAlex ID: W1984706147
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description: scientific article; zbMATH DE number 4144133