Hasse-Witt matrices for the Fermat curves of prime degree
type: Item
instance of: scholarly article
title: Hasse-Witt matrices for the Fermat curves of prime degree
zbMATH Open document ID: 0894.14010
author: Josep González
published in: Tôhoku Mathematical Journal. Second Series
publication date: 1997-08-28T00:00:00Z
review text: Let \(C\) be a smooth projective curve of genus \(g>0\) defined over an algebraically closed field of characteristic \(p>0\). The Hasse-Witt invariant \(r(C)\) of \(C\) is the maximum number of cyclic unramified independent extensions of degree \(p\) of the function field \(k(C)\). In this paper the Hasse-Witt invariants \(r(C_\ell)\) are computed for the family of curves \(C_\ell\) defined by the equation \(Y^\ell= F(X)\), where \(\ell\) is a prime and \(F(X)\in k[X]\) is a separable polynomial of degree \(n\). This family includes hyperelliptic curves \((\ell=2,\;n>2)\) and Fermat curves (when \(F(X)= X^\ell+1)\).
Mathematics Subject Classification ID: 14H05
Mathematics Subject Classification ID: 14G15
Mathematics Subject Classification ID: 14H45
zbMATH DE Number: 1054460
zbMATH Keywords: characteristic \(p\)
zbMATH Keywords: Hasse-Witt invariant
zbMATH Keywords: function field
zbMATH Keywords: hyperelliptic curves
zbMATH Keywords: Fermat curves
reviewed by: A. Del Centina
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.2748/tmj/1178225144
OpenAlex ID: W2010309257
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DOI: 10.2748/TMJ/1178225144
description: scientific article; zbMATH DE number 1054460