### Torsion points of abelian varieties in abelian extensions, by Wolfgang M. Ruppert

Let A be an abelian variety defined over a number field K and
let Kab be the maximal abelian extension of K. We show that there
only finitely many torsion points of A which are defined over Kab
iff A has no abelian subvariety with complex multiplication over K.
We use this to give another proof of Ribet's result that A has
only finitely many torsion points which are defined over
the cyclotomic extension of K.

Wolfgang M. Ruppert <ruppert@exp-math.uni-essen.de>