Arbitrarily large p-torsion in Tate-Shafarevich groups

We show that, for any prime p, there exist absolutely simple abelian varieties over Q with arbitrarily large p-torsion in their Tate-Shafarevich groups. To prove this, we construct explicit µp-covers of Jacobians of curves of the form y p = x(x − 1)(x − a) which violate the Hasse principle. In the a...

Бүрэн тодорхойлолт

Номзүйн дэлгэрэнгүй
Үндсэн зохиолчид: Flynn, E, Shnidman, A, Fisher, T
Формат: Journal article
Хэл сонгох:English
Хэвлэсэн: Cambridge University Press 2024