On characteristic power series of dual signed Selmer groups
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2022
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| _version_ | 1866909206298230784 |
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| author | Ray, Jishnu Sprung, Florian |
| author_facet | Ray, Jishnu Sprung, Florian |
| contents | We relate the cardinality of the $p$-primary part of the Bloch-Kato Selmer group over $\mathbb{Q}$ attached to a modular form at a non-ordinary prime $p$ to the constant term of the characteristic power series of the signed Selmer groups over the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$. This generalizes a result of Vigni and Longo in the ordinary case. In the case of elliptic curves, such results follow from earlier works by Greenberg, Kim, the second author, and Ahmed-Lim, covering both the ordinary and most of the supersingular case. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2205_04671 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | On characteristic power series of dual signed Selmer groups Ray, Jishnu Sprung, Florian Number Theory Primary: 11R23, Secondary: 11R18, 11F11, 11F85 We relate the cardinality of the $p$-primary part of the Bloch-Kato Selmer group over $\mathbb{Q}$ attached to a modular form at a non-ordinary prime $p$ to the constant term of the characteristic power series of the signed Selmer groups over the cyclotomic $\mathbb{Z}_p$-extension of $\mathbb{Q}$. This generalizes a result of Vigni and Longo in the ordinary case. In the case of elliptic curves, such results follow from earlier works by Greenberg, Kim, the second author, and Ahmed-Lim, covering both the ordinary and most of the supersingular case. |
| title | On characteristic power series of dual signed Selmer groups |
| topic | Number Theory Primary: 11R23, Secondary: 11R18, 11F11, 11F85 |
| url | https://arxiv.org/abs/2205.04671 |