Torsion Points of Abelian Varieties with Values in Infinite Extensions over a -adic Field
Yoshiyasu Ozeki
Kyoto University, Japan
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Abstract
Let be an abelian variety over a -adic field and an algebraic infinite extension over . We consider the finiteness of the torsion part of the group of rational points under some assumptions. In 1975, Hideo Imai proved that such a group is finite if has good reduction and is the cyclotomic -extension of . In this paper, first we show a generalization of Imai’s result in the case where has good ordinary reduction. Next we give some finiteness results when is an elliptic curve and is the field generated by the -th power torsion of an elliptic curve.
Cite this article
Yoshiyasu Ozeki, Torsion Points of Abelian Varieties with Values in Infinite Extensions over a -adic Field. Publ. Res. Inst. Math. Sci. 45 (2009), no. 4, pp. 1011–1031
DOI 10.2977/PRIMS/1260476651