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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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References

Dixon, J. D., du Sautoy, M. P. F., Mann, A. and Segal, D., Analytic pro-p groups, 2nd edn, Cambridge Studies in Advanced Mathematics, Volume 61 (Cambridge University Press, Cambridge, 1999).Google Scholar
Fehm, Arno, Jarden, Moshe and Petersen, Sebastian, Kuykian fields. Forum Math., 2010..Google Scholar
Fried, Michael D. and Jarden, Moshe, Field arithmetic, in Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge, 2nd edn, A Series of Modern Surveys in Mathematics, Volume 11 (Springer-Verlag, Berlin, 2005).Google Scholar
Huppert, B., Endliche Gruppen I, Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Volume 134 (Springer, Berlin, 1967).Google Scholar
Jarden, Moshe, Diamonds in torsion of Abelian varieties, J. Inst. Math. Jussieu 9 (3) (2010), 477–480.Google Scholar
Larsen, Michael J. and Pink, Richard, Finite subgroups of algebraic groups, J. Amer. Math. Soc. 24 (4) (2011), 1105–1158.Google Scholar