Arbitrarily large p-torsion in Tate-Shafarevich groups

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...

書目詳細資料
Main Authors:	Flynn, E, Shnidman, A, Fisher, T
格式:	Journal article
語言:	English
出版:	Cambridge University Press 2024

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