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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 assumptio...ns. 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 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.続きを見る
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