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 ℤ_p_-extension of K. In this paper, first we show a generalization of Imai’s result in the case where A has good ordinary reduction. Next we give some finiteness results when A is an elliptic curve and L is the field generated by the p-th power torsion of an elliptic curve.
Cite this article
Yoshiyasu Ozeki, Torsion Points of Abelian Varieties with Values in Infinite Extensions over a <i>p</i>-adic Field. Publ. Res. Inst. Math. Sci. 45 (2009), no. 4, pp. 1011–1031DOI 10.2977/PRIMS/1260476651