Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2402.07317 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866914674627313664 |
|---|---|
| author | Tamiozzo, Matteo |
| author_facet | Tamiozzo, Matteo |
| contents | We prove, under suitable assumptions, that $p$-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 $p$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07317 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Congruences of modular forms and modularity of Tate-Shafarevich classes Tamiozzo, Matteo Number Theory We prove, under suitable assumptions, that $p$-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 $p$. |
| title | Congruences of modular forms and modularity of Tate-Shafarevich classes |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.07317 |