@article{3f8e63226e944f1eb4ed131ebd361565,
title = "Diamonds in torsion of Abelian varieties",
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.",
keywords = "Abelian varieties, Galois groups, Haran's diamond theorem, Hilbertian fields, number fields, torsion points",
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.",
year = "2010",
month = jul,
doi = "10.1017/S1474748009000255",
language = "אנגלית",
volume = "9",
pages = "477--480",
journal = "Journal of the Institute of Mathematics of Jussieu",
issn = "1474-7480",
publisher = "Cambridge University Press",
number = "3",
}