Selmer ranks in twists of CM abelian varieties
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909712581132288 |
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| author | Shu, Jie |
| author_facet | Shu, Jie |
| contents | We prove the Selmer ranks in certain families of $p$-th twists of CM abelian varieties obey the symplectic or unitary distributions. As an application, for a prime $p\geq 3$, we obtain that the twisted Fermat curves $X^p+Y^p=δ$ over a number field containing a primitive $p$-th root of unity are ``largely" unsolvable as $δ$ varies. We also discuss the rank growth in cyclic extensions of prime degree for CM abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_21274 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Selmer ranks in twists of CM abelian varieties Shu, Jie Number Theory Primiary 11G10, Secondary 11G05, 11G30, 11D41, 14K22 We prove the Selmer ranks in certain families of $p$-th twists of CM abelian varieties obey the symplectic or unitary distributions. As an application, for a prime $p\geq 3$, we obtain that the twisted Fermat curves $X^p+Y^p=δ$ over a number field containing a primitive $p$-th root of unity are ``largely" unsolvable as $δ$ varies. We also discuss the rank growth in cyclic extensions of prime degree for CM abelian varieties. |
| title | Selmer ranks in twists of CM abelian varieties |
| topic | Number Theory Primiary 11G10, Secondary 11G05, 11G30, 11D41, 14K22 |
| url | https://arxiv.org/abs/2504.21274 |