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Abelian varieties and Galois extensions of Hilbertian fields

Published online by Cambridge University Press:  16 May 2012

Christopher Thornhill
Christopher Thornhill*
Affiliation:
Department of Mathematics, Indiana University, Bloomington, IN 47405, USA ([email protected])
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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 $K({A}_{\mathrm{tor} } )$.

Keywords

Abelian varietiesHilbertian fieldsGalois groups
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 12 , Issue 2 , April 2013 , pp. 237 - 247
Copyright
©Cambridge University Press 2012

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