Torsion points of abelian varieties with values in infinite extensions over a p-adic field

Abstract

Let A be an abelian variety over a p-adic field K and L an algebraic infinite extension over K. We consider the finiteness of the torsion part of the group of rational points A(L) under some assumptions. In 1975, Hideo Imai proved that such a group is finite if A has good reduction and L is the cyclotomic Zp-extension of K. In this talk, first we show a generalization of Imai’s result in the case where A has ordinary good reduction. Next we give some finiteness results when A is an elliptic curve and L is the field generated by the p-power torsion of an elliptic curve.

Cite this paper

@inproceedings{Ozeki2008TorsionPO, title={Torsion points of abelian varieties with values in infinite extensions over a p-adic field}, author={Yoshiyasu Ozeki}, year={2008} }