Bounds on the ranks of Mordell-Weil groups of abelian varieties over extensions of function fields
代数学セミナー
開催期間
2011.8.22(月)
00:00 ~ 17:00
00:00 ~ 17:00
場所
伊都キャンパス 伊都図書館3階 小講義室 2
講演者
Ambrus Pal （Imperial College London）
概要
We prove a new upper bound on the ranks of Mordell-Weil groups
of abelian varieties over function fields after regular
geometrically Galois extensions of the base field
which applies to fields of arbitrary characteristic,
improving on previous results of Silverman, Ellenberg and Pacheco.
We use Hodge theory to prove an even stronger bound for elliptic curves
when the base field has characteristic zero.