Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties
We show that, for any d, the 2-torsion of Tate-Shafarevich groups of absolutely simple abelian varieties of dimension d over Q can be arbitrarily large. This involves the use of an approach, which we shall describe, for demonstrating arbitrarily large Tate-Shafarevich groups which does not req...
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| 格式: | Journal article |
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Polskiej Akademii Nauk
2019
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| _version_ | 1826263059379781632 |
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| author | Flynn, E |
| author_facet | Flynn, E |
| author_sort | Flynn, E |
| collection | OXFORD |
| description | We show that, for any d, the 2-torsion of Tate-Shafarevich groups of absolutely simple abelian varieties of dimension d over Q can be arbitrarily large. This involves the use of an approach, which we shall describe, for demonstrating arbitrarily large Tate-Shafarevich groups which does not require entire Selmer groups to be found. |
| first_indexed | 2024-03-06T19:45:40Z |
| format | Journal article |
| id | oxford-uuid:22383ccd-250e-4c3b-a4a7-62a995e01a1b |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:45:40Z |
| publishDate | 2019 |
| publisher | Polskiej Akademii Nauk |
| record_format | dspace |
| spelling | oxford-uuid:22383ccd-250e-4c3b-a4a7-62a995e01a1b2022-03-26T11:37:32ZArbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varietiesJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:22383ccd-250e-4c3b-a4a7-62a995e01a1bSymplectic Elements at OxfordPolskiej Akademii Nauk2019Flynn, EWe show that, for any d, the 2-torsion of Tate-Shafarevich groups of absolutely simple abelian varieties of dimension d over Q can be arbitrarily large. This involves the use of an approach, which we shall describe, for demonstrating arbitrarily large Tate-Shafarevich groups which does not require entire Selmer groups to be found. |
| spellingShingle | Flynn, E Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties |
| title | Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties |
| title_full | Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties |
| title_fullStr | Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties |
| title_full_unstemmed | Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties |
| title_short | Arbitrarily large 2-torsion in Tate-Shafarevich groups of Abelian varieties |
| title_sort | arbitrarily large 2 torsion in tate shafarevich groups of abelian varieties |
| work_keys_str_mv | AT flynne arbitrarilylarge2torsionintateshafarevichgroupsofabelianvarieties |