Congruences of modular forms and modularity of Tate-Shafarevich classes
Number Theory
2024-02-13 v1
Abstract
We prove, under suitable assumptions, that -torsion Tate-Shafarevich classes for elliptic curves over the rationals are visible in quotients of Jacobians of modular curves, as predicted by a conjecture of Jetchev-Stein. The key ingredient is the non-triviality of the Bertolini-Darmon bipartite Kolyvagin system, which implies that suitable cohomology classes of the system form a basis of the Selmer group modulo .
Cite
@article{arxiv.2402.07317,
title = {Congruences of modular forms and modularity of Tate-Shafarevich classes},
author = {Matteo Tamiozzo},
journal= {arXiv preprint arXiv:2402.07317},
year = {2024}
}