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.