Diamonds in Torsion of Abelian Varieties.

Diamonds in Torsion of Abelian Varieties.

Thu, 21/05/2009
17:00 		Moshe Jarden (Tel Aviv) Logic Seminar Add to calendar L3
Diamonds in Torsion of Abelian Varieties.
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(A_\tor) $ is Hilbertian. We prove our conjecture when $ K $ is a number field. The proofs applies a result of Serre about $ l $-torsion of Abelian varieties, information about $ l $-adic analytic groups, and Haran's diamond theorem.