Diamonds in torsion of Abelian varieties

Moshe Jarden

doi:10.1017/S1474748009000255

Diamonds in torsion of Abelian varieties

Moshe Jarden

School of Mathematical Sciences

Research output: Contribution to journal › Article › peer-review

Abstract

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 language	English
Pages (from-to)	477-480
Number of pages	4
Journal	Journal of the Institute of Mathematics of Jussieu
Volume	9
Issue number	3
DOIs	https://doi.org/10.1017/S1474748009000255
State	Published - Jul 2010

Keywords

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

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10.1017/S1474748009000255

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abstract = "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.",

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author = "Moshe Jarden",

note = "Funding Information: Acknowledgements. Research supported by the Minkowski Center for Geometry at Tel Aviv University, established by the Minerva Foundation, by an ISF grant, and by the European Community Marie Curie Research Training Network GTEM.",

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N2 - 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.

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KW - Galois groups

KW - Haran's diamond theorem

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Diamonds in torsion of Abelian varieties

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Keywords

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