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

by Prof. Yuichiro Taguchi (Kyoto University, Japan)

Thursday 1 Nov 2012, 16:00 → 17:00 Asia/Kolkata

AG-69 (Colaba Campus)

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.