Rational Torsion Research Articles

Curves of genus $2$ with a rational torsion divisor of order $23$

Curves of genus $2$ with a rational torsion divisor of order $23$

Sequences of rational torsions on abelian varieties

We address the question of how fast the available rational torsion on abelian varieties over ℚ increases with dimension. The emphasis will be on the derivation of sequences of torsion divisors on hyperelliptic curves. Work of Hellegouarch and Lozach (and Klein) may be made explicit to provide sequences of curves with rational torsion divisors of orders increasing linearly with respect to genus. The main results in §2) are applications of a new technique which provide sequences of hyperelliptic curves for all torsions in an interval [a g ,a g +b g ]] wherea g is quadratic ing andb g is linear ing. As well as providing an improvement from linear to quadratic, these results provide a wide selection of torsion orders for potential use by those involved in computer integration. We conclude by considering possible techniques for divisors of non-hyperelliptic curves, and for general abelian varieties.

Large rational torsion on Abelian varieties

A method of searching for large rational torsion on Abelian varieties is described. A few explicit applications of this method over Q give rational 11- and 13-torsion in dimension 2, and rational 29-torsion in dimension 4.

Rational torsion in complex-multiplication elliptic curves

Let E be an elliptic curve with complex multiplication, j its j-invariant, F its multiplication field, L = Q( j), and H = F( j). A complete tabulation is given of the possible torsion of E rational over L or over H.

Is J 1 a Subgroup of the Monster?

Bulletin of the London Mathematical SocietyVolume 18, Issue 4 p. 349-350 Notes and papers Is J1 a Subgroup of the Monster? Robert A. Wilson, Robert A. Wilson Department of Pure Mathematics and Mathematical Statistics University of Cambridge, 16 Mill Lane Cambridge CB2 1SBSearch for more papers by this author Robert A. Wilson, Robert A. Wilson Department of Pure Mathematics and Mathematical Statistics University of Cambridge, 16 Mill Lane Cambridge CB2 1SBSearch for more papers by this author First published: July 1986 https://doi.org/10.1112/blms/18.4.349Citations: 5AboutRelatedInformationPDFPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessClose modalShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL No abstract is available for this article.Citing Literature Volume18, Issue4July 1986Pages 349-350 RelatedInformation RecommendedIs the Suzuki group Sz(8) a subgroup of the Monster?Robert A. Wilson, Bulletin of the London Mathematical SocietyStructure of the cuspidal rational torsion subgroup of J1(pn)Yifan Yang, Jeng-Daw Yu, Journal of the London Mathematical SocietySubgroup Families Controlling p-Local Finite GroupsCarles Broto, Natàlia Castellana, Jesper Grodal, Ran Levi, Bob Oliver, Proceedings of the London Mathematical SocietyPSL2(59) is a Subgroup of the MonsterPetra E. Holmes, Robert A. Wilson, Journal of the London Mathematical SocietyThe uniqueness of PSU 3(8) in the MonsterRobert A. Wilson, Bulletin of the London Mathematical Society