Torsion points of abelian varieties with values in infinite extensions over a p-adic field - Collections

＜preprint＞
Torsion points of abelian varieties with values in infinite extensions over a p-adic field

Creator	Author PID L004376 Creator Name Ozeki, Yoshiyasu 小関, 祥康オゼキ, ヨシヤス Affiliation Affiliation Name Faculty of Mathematics, Kyushu University 九州大学大学院数理学研究院
Language	English
Publisher	Faculty of Mathematics, Kyushu University
Publisher	九州大学大学院数理学研究院
Date	2008-10-24
Source Title	MI Preprint Series
Vol	2008-5
Publication Type	Author's Original
Access Rights	open access
Related DOI	MI Preprint Series \|\| 2008-5 \|\| p1-17
Related DOI	http://www.math.kyushu-u.ac.jp/
Related URI	MI Preprint Series \|\| 2008-5 \|\| p1-17
Related URI	http://www.math.kyushu-u.ac.jp/
Relation	MI Preprint Series \|\| 2008-5 \|\| p1-17
Relation	http://www.math.kyushu-u.ac.jp/
Abstract	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 assumptio...ns. In 1975, Hideo Imai proved that such a group is finite if A has good reduction and L is the cyclotomic Z_p-extension of K. In this paper, 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.show more

File	FileType	Size	Views	Description
MI2008-5	pdf	270 KB	252

Record ID	12550
Peer-Reviewed	Unrefereed
Notes	MI: Global COE Program Education-and-Research Hub for Mathematics-for-Industry
Notes	グローバルCOEプログラム「マス･フォア･インダストリ教育研究拠点」
Type	プレプリント
Created Date	2009.04.22
Modified Date	2018.02.20