Main conjectures for non-CM elliptic curves at good ordinary primes
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arXiv
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| Format: | Preprint |
| Published: |
2024
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| _version_ | 1866914273880440832 |
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| author | Yan, Xiaojun Zhu, Xiuwu |
| author_facet | Yan, Xiaojun Zhu, Xiuwu |
| contents | Let $E/\mathbb{Q}$ be an elliptic curve and $p > 2$ be a prime of good ordinary reduction for $E$. Assume that the residue representation associated with $(E, p)$ is irreducible. In this paper, we prove more cases on several Iwasawa main conjectures for $E$. As applications, we prove more general cases of $p$-converse theorem and $p$-part BSD formula when the rank is less than or equal to $1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_20078 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Main conjectures for non-CM elliptic curves at good ordinary primes Yan, Xiaojun Zhu, Xiuwu Number Theory 11G40, 11G05, 11R23 Let $E/\mathbb{Q}$ be an elliptic curve and $p > 2$ be a prime of good ordinary reduction for $E$. Assume that the residue representation associated with $(E, p)$ is irreducible. In this paper, we prove more cases on several Iwasawa main conjectures for $E$. As applications, we prove more general cases of $p$-converse theorem and $p$-part BSD formula when the rank is less than or equal to $1$. |
| title | Main conjectures for non-CM elliptic curves at good ordinary primes |
| topic | Number Theory 11G40, 11G05, 11R23 |
| url | https://arxiv.org/abs/2412.20078 |