Kuykian fields

Arno Fehm*, Moshe Jarden, Sebastian Petersen

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


The Kuykian conjecture for a Hilbertian field K says that if A/K is an abelian variety, then every intermediate field of K(A tor)/K is Hilbertian. We prove the Kuykian conjecture in the following cases: (a) K is finitely generated (over its prime field). (b) K D F s [σ] for almost all ε 2 Gal(K) e, where F is a finitely generated field. (c) K D F ins, where F is the quotient field of a complete local domain of dimension at least 2.

Original languageEnglish
Pages (from-to)1013-1022
Number of pages10
JournalForum Mathematicum
Issue number5
StatePublished - Sep 2012


  • Abelian varieties
  • Hilbertian fields
  • Torsion points


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