Torsion points of abelian varieties with values in infinite extensions over a p-adic field
| dc.creator | Ozeki, Yoshiyasu | |
| dc.date | 2008-09-24 | |
| dc.date.accessioned | 2026-07-07T10:04:53Z | |
| dc.date.available | 2026-07-07T10:04:53Z | |
| dc.description | Let $A$ be an abelian variety over a $p$-adic field $K$ and $L$ an algebraic infinite extension over $K$. We consider the finiteness of the torsion part of the group of rational points $A(L)$ under some assumptions. In 1975, Hideo Imai proved that such a group is finite if $A$ has good reduction and $L$ is the cyclotomic $\mathbb{Z}_p$-extension of $K$. In this talk, first we show a generalization of Imai's result in the case where $A$ has ordinary good reduction. Next we give some finiteness results when $A$ is an elliptic curve and $L$ is the field generated by the $p$-power torsion of an elliptic curve. | |
| dc.identifier | https://arxiv.org/abs/0809.4061 | |
| dc.identifier | http://arxiv.org/abs/0809.4061 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/169846 | |
| dc.subject | Number Theory | |
| dc.title | Torsion points of abelian varieties with values in infinite extensions over a p-adic field | |
| dc.type | text |