Conditions related to \(\pi_1\) of projective curves
type: Item
instance of: scholarly article
title: Conditions related to \(\pi_1\) of projective curves
zbMATH Open document ID: 0943.14013
author: Katherine F. Stevenson
published in: Journal of Number Theory
publication date: 2000-09-03T00:00:00Z
review text: Let \(D\) be a curve of genus \(g\) over an algebraically closed field of positive characteristic \(p\). We write \(\pi_A(D)\) for the set of isomorphism classes of of finite groups occurring as Galois groups of unramified covers of \(D\). This paper is concerned with giving necessary and sufficient conditions for a family of groups to lie in \(\pi_A(D)\). The main tool is a criterion of Nakajima concerning generators of group rings. The author first reviews the known results and gives a comparison between some necessary conditions. In particular, she shows that for many groups, Nakajima's criterion does not follow from previously known criteria. Then the author goes on to consider a specific class of groups for which she shows that Nakajima's condition is not only necessary but also sufficient. In the last section more specific results about tame covers of genus two curves are derived.
Mathematics Subject Classification ID: 14H30
Mathematics Subject Classification ID: 14E20
Mathematics Subject Classification ID: 14G32
Mathematics Subject Classification ID: 14F35
zbMATH DE Number: 1207953
zbMATH Keywords: fundamental group
zbMATH Keywords: positive characteristic
zbMATH Keywords: projective curves
zbMATH Keywords: tame covers
zbMATH Keywords: Galois groups
reviewed by: Martin J. Pikaart
MaRDI profile type: Publication
full work available at URL: jnth.1997.2193
OpenAlex ID: W1981516663
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DOI: 10.1006/JNTH.1997.2193
description: scientific article; zbMATH DE number 1207953