Abstract
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 up-covers of Jacobians of curves of the form yp = x(x-1)(x-A) which violate the Hasse principle. In the appendix, Tom Fisher explains how to interpret our proof in terms of a Cassels-Tate pairing.
Original language | English |
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Journal | Journal of the Institute of Mathematics of Jussieu |
DOIs | |
State | Accepted/In press - 2024 |
Keywords
- abelian variety
- Tate-Shafarevich group
All Science Journal Classification (ASJC) codes
- General Mathematics