Diamonds in torsion of Abelian varieties

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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
Issue number3
StatePublished - Jul 2010


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


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