Abelian constraints in inverse Galois theory
type: Item
instance of: scholarly article
title: Abelian constraints in inverse Galois theory
zbMATH Open document ID: 1197.12003
author: Anna Cadoret
author: Pierre Dèbes
published in: Manuscripta Mathematica
publication date: 2009-03-26T00:00:00Z
review text: Let \(k\) be a field, \(B\) a \(k\)-curve (i.e. a smooth projective and geometrically connected \(k\)-scheme of dimension 1), \(G\) a finite group, \(f:Y\to B\) a \(k\)-\(G\)-cover of curves with group \(G\) and ramification indices \(e_1,\dots,e_r\) and let \(P\) be ant subgroup of \(G\) of index \(m.\) Assume that the branch divisor of \(f:Y\to B\) has good reduction and that \(l=ch(K)\) does not divide \((|G|,m!).\) It is shown that the order of \(\mathbb{P}^{ab}\) is bounded by a constant depending on \(m, r\) and the smallest prime \(l\) not dividing \(|G|\) of good reduction of the branch divisor. It is conjectured that the orders of \(\mathbb{P}^{ab}\) are bounded by a constant depending only on \(r\) and \(m\). The connection with other conjectures is discussed.
reviewed by: Cristodor-Paul Ionescu
Mathematics Subject Classification ID: 12F12
Mathematics Subject Classification ID: 14H30
zbMATH DE Number: 5533199
zbMATH Keywords: Inverse Galois theory
zbMATH Keywords: Galois cover.
MaRDI profile type: Publication
full work available at URL: s00229-008-0236-1
OpenAlex ID: W1973477277
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DOI: 10.1007/S00229-008-0236-1
description: scientific article; zbMATH DE number 5533199