Hostname: page-component-586b7cd67f-rcrh6 Total loading time: 0 Render date: 2024-11-25T09:43:19.213Z Has data issue: false hasContentIssue false
  • English
  • Français

Diamonds in Torsion of Abelian Varieties

Part of: General field theory

Published online by Cambridge University Press:  10 February 2010

Moshe Jarden
Moshe Jarden
Affiliation:
School of Mathematics, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel ([email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

A theorem of Kuyk says that every Abelian extension of a Hilbertian field is Hilbertian. We conjecture that for an Abelian variety A defined over a Hilbertian field K every extension L of K in K(Ator) is Hilbertian. We prove our conjecture when K is a number field. The proof applies a result of Serre about l-torsion of Abelian varieties, information about l-adic analytic groups, and Haran's diamond theorem.

Keywords

Abelian varietiestorsion pointsnumber fieldsGalois groupsHilbertian fieldsHaran's diamond theorem

MSC classification

Secondary: 12E30: Field arithmetic
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 9 , Issue 3 , July 2010 , pp. 477 - 480
Copyright
Copyright © Cambridge University Press 2010

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Fried, M. D. and Jarden, M., Field arithmetic, 3rd edn (revised by M. Jarden), Ergebnisse der Mathematik (3), Volume 11 (Springer, 2008).Google Scholar
2.Serre, J.-P., Résumé des cours de 1985–1986 (Annuaire du Collège de France, Paris, 1986).Google Scholar
3.Mumford, D., Abelian varieties (Oxford University Press, 1974).Google Scholar