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Abelian varieties and Galois extensions of Hilbertian fields

  • Christopher Thornhill (a1)

Abstract

In a recent paper Moshe Jarden (Diamonds in torsion of Abelian varieties, J. Inst. Math. Jussieu9(3) (2010), 477–480) proposed a conjecture, later named the Kuykian conjecture, which states that if $A$ is an Abelian variety defined over a Hilbertian field $K$ , then every intermediate field of $K({A}_{\mathrm{tor} } )/ K$ is Hilbertian. We prove that the conjecture holds for Galois extensions of $K$ in $K({A}_{\mathrm{tor} } )$ .

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Fehm, Arno, Jarden, Moshe and Petersen, Sebastian, Kuykian fields. Forum Math., 2010..
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Jarden, Moshe, Diamonds in torsion of Abelian varieties, J. Inst. Math. Jussieu 9 (3) (2010), 477480.
Larsen, Michael J. and Pink, Richard, Finite subgroups of algebraic groups, J. Amer. Math. Soc. 24 (4) (2011), 11051158.
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Abelian varieties and Galois extensions of Hilbertian fields

  • Christopher Thornhill (a1)

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