Non-conservative function fields of genus \((p+1)/2\)
type: Item
instance of: scholarly article
title: Non-conservative function fields of genus \((p+1)/2\)
zbMATH Open document ID: 0699.14031
DOI: 10.1007/BF02568482
author: Maria Lucia Torres Villela
author: Karl-Otto Stöhr
published in: Manuscripta Mathematica
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/155459
review text: Let \(F/K\) be a separably generated function field in one variable of genus \(g\) and positive characteristic \(p\geq 5\). It is called conservative if \(g=\bar g=\) genus of \(F\bar K/\bar K\) \((\bar K=\) algebraic closure of \(K\)). The defect \(g-\bar g\) is always divisible by \((p-1)/2\). The authors study the first nontrivial case where \(\bar g=1\) and \(g=(p+1)/2\). In their main result, they describe a normal form for such \(F/K\), and moreover, they give criteria for \(F/K\) to be hyperelliptic, and compute its automorphism group.
reviewed by: Ernst-Ulrich Gekeler
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 14H45
Mathematics Subject Classification ID: 14H52
zbMATH DE Number: 4146126
zbMATH Keywords: non-conservative function field
zbMATH Keywords: hyperelliptic function field
zbMATH Keywords: genus
MaRDI profile type: Publication
cites work: Q5590141
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description: scientific article; zbMATH DE number 4146126