p-Selmer ranks of CM abelian varieties
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866911773111615488 |
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| author | Bell, Jamie |
| author_facet | Bell, Jamie |
| contents | For an elliptic curve with complex multiplication over a number field, the $p^{\infty}$--Selmer rank is even for all $p$. Česnavičius proved this using the fact that $E$ admits a $p$-isogeny whenever $p$ splits in the complex multiplication field, and invoking known cases of the $p$-parity conjecture. We give a direct proof, and generalise the result to abelian varieties. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2208_14563 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | p-Selmer ranks of CM abelian varieties Bell, Jamie Number Theory 11G15 (Primary) 14K22 (Secondary) For an elliptic curve with complex multiplication over a number field, the $p^{\infty}$--Selmer rank is even for all $p$. Česnavičius proved this using the fact that $E$ admits a $p$-isogeny whenever $p$ splits in the complex multiplication field, and invoking known cases of the $p$-parity conjecture. We give a direct proof, and generalise the result to abelian varieties. |
| title | p-Selmer ranks of CM abelian varieties |
| topic | Number Theory 11G15 (Primary) 14K22 (Secondary) |
| url | https://arxiv.org/abs/2208.14563 |