Seminar series
Date
Thu, 21 May 2009
17:00
17:00
Location
L3
Speaker
Moshe Jarden
Organisation
Tel Aviv
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.