Speaker: Yuichiro Taguchi
Date: November 01, 2012
Affiliation: Kyoto University, Japan

Abstract: We extend the following theorem of H. Imai in several ways: If $A$ is an abelian variety with potentially good reduction over a finite extension $K$ of $Q_p$, then it has only finitely many rational torsion points over the maximal p-cyclotomic extension of $K$. In particular, we prove the finiteness over $K(K^{1/p^\infty})$. It has applications in Iwasawa theory.