On supersingular abelian varieties of dimension two over finite fields
type: Item
instance of: scholarly article
title: On supersingular abelian varieties of dimension two over finite fields
zbMATH Open document ID: 0923.11091
published in: Finite Fields and their Applications
publication date: 1998-04-26T00:00:00Z
review text: Let \(A\) be an abelian variety over a finite field \(k\) of characteristic \(p>0\). The fact that \(A\) is supersingular, i.e. the group of \(p\)-torsion points on \(A\) is trivial, can be expressed in terms of the characteristic polynomial of the Frobenius endomorphism of \(A\) over the finite field \(k\). The author gives a list of all these characteristic polynomials for supersingular abelian varieties \(A\) of dimension 2. In addition he shows which of these abelian varieties are isogenous to Jacobians of curves. Then he studies the group structure of the \(k\) rational points \(A(k)\) in these cases.
Mathematics Subject Classification ID: 11G10
Mathematics Subject Classification ID: 11G20
Mathematics Subject Classification ID: 14G05
Mathematics Subject Classification ID: 14H40
zbMATH DE Number: 1144295
zbMATH Keywords: finite fields
zbMATH Keywords: \(k\) rational points
zbMATH Keywords: characteristic polynomials
zbMATH Keywords: supersingular abelian varieties
zbMATH Keywords: Jacobians
author: Chaoping Xing
MaRDI profile type: Publication
full work available at URL: ffta.1996.0024
OpenAlex ID: W1992986704
DOI: 10.1006/FFTA.1996.0024
description: scientific article; zbMATH DE number 1144295