# Colloquium abstracts

**Yuichiro Taguchi**

Kyoto University, Japan

November 1, 2012

**Rational torsion points of abelian varieties over a large extension of a local field**: 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.