A note on the supersingular \(K3\) surface of Artin invariant 1
type: Item
instance of: scholarly article
title: A note on the supersingular \(K3\) surface of Artin invariant 1
zbMATH Open document ID: 1250.14024
author: Matthias Schütt
published in: Journal of Pure and Applied Algebra
publication date: 2012-10-16T00:00:00Z
full work available at URL: https://arxiv.org/abs/1105.4993
reviewed by: Noriko Yui
Mathematics Subject Classification ID: 14J28
Mathematics Subject Classification ID: 11G25
Mathematics Subject Classification ID: 14G15
zbMATH DE Number: 6094130
zbMATH Keywords: supersingular \(K3\) surface
zbMATH Keywords: Artin invariant
zbMATH Keywords: Picard number
MaRDI profile type: Publication
OpenAlex ID: W2131118190
arXiv ID: 1105.4993
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DOI: 10.1016/J.JPAA.2011.10.036
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review text: This paper is concerned with the supersingular \(K3\) surface \(X\) of Artin invariant \(1\) in characteristic \(p>0\), where \(p\) is an arbitrary prime. Over the algebraic closure \(\overline{{\mathbb{F}}_p}\), such a \(K3\) surface is unique. The main result is this paper is the following theorem.NEWLINENEWLINETheorem. The supersingular \(K3\) surface \(X\) with Artin invariant \(1\) admits a model over the prime field \({\mathbb{F}}_p\) with Picard number \(21\).NEWLINENEWLINEThis model attains the Picard number \(22\) over the quadratic extension \({\mathbb{F}}_{p^2}\), but this maximum can never attained over \({\mathbb{F}}_{p^e}\) for any odd \(e\).
description: scientific article; zbMATH DE number 6094130