Diamonds in torsion of Abelian varieties

Moshe Jarden*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations

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.

Original languageEnglish
Pages (from-to)477-480
Number of pages4
JournalJournal of the Institute of Mathematics of Jussieu
Volume9
Issue number3
DOIs
StatePublished - Jul 2010

Funding

FundersFunder number
European Community Marie Curie Research Training Network GTEM
Minerva Foundation
Israel Science Foundation

    Keywords

    • Abelian varieties
    • Galois groups
    • Haran's diamond theorem
    • Hilbertian fields
    • number fields
    • torsion points

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