A generalization of a theorem of Imai and its applications to Iwasawa theory

Abstract

It is proved that, if $K$ is a complete discrete valuation field of mixed characteristic $(0,p)$ with residue field satisfying a mild condition, then any abelian variety over $K$ with potentially good reduction has finite $K(K^{1/p^\infty})$-rational torsion subgroup. This can be used to remove certain conditions assumed in some theorems in Iwasawa theory.