Torsion points of abelian varieties in abelian extensions
Number Theory
2007-05-23 v1
Abstract
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.
Keywords
Cite
@article{arxiv.math/9803169,
title = {Torsion points of abelian varieties in abelian extensions},
author = {Wolfgang M. Ruppert},
journal= {arXiv preprint arXiv:math/9803169},
year = {2007}
}