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

Seminar series

Number Theory Seminar

Date

Tue, 25 Sep 2012

Time

14:00 - 14:40

Location

Speaker

Yuichiro Taguchi

Organisation

Kyushu University

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 $\mathbf{Q}_p$, then it has only finitely many rational torsion points over the maximal $p$-cyclotomic extension of $K$. In particular, we prove the finiteness over $K(K^{1/p^\infty})$.