On characteristic elements modulo $p$ in non-commutative Iwasawa theory
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866910928705945600 |
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| author | Lim, Meng Fai Qin, Chao |
| author_facet | Lim, Meng Fai Qin, Chao |
| contents | Coates, Fukaya, Kato, Sujatha and Venjakob come up with a procedure of attaching suitable characteristic element to Selmer groups defined over a non-commutative $p$-adic Lie extension, which is subsequently refined by Burns and Venjakob. By their construction, these characteristic elements are realized as elements in an appropriate localized $K_1$-group. In this paper, we will introduce a notion of modulo $p$ for these elements and study some of their properties. As an application, we study the Greenberg Selmer group of a tensor product of modular forms, where $p$ is an Eisenstein prime for one of these forms. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_13812 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On characteristic elements modulo $p$ in non-commutative Iwasawa theory Lim, Meng Fai Qin, Chao Number Theory Coates, Fukaya, Kato, Sujatha and Venjakob come up with a procedure of attaching suitable characteristic element to Selmer groups defined over a non-commutative $p$-adic Lie extension, which is subsequently refined by Burns and Venjakob. By their construction, these characteristic elements are realized as elements in an appropriate localized $K_1$-group. In this paper, we will introduce a notion of modulo $p$ for these elements and study some of their properties. As an application, we study the Greenberg Selmer group of a tensor product of modular forms, where $p$ is an Eisenstein prime for one of these forms. |
| title | On characteristic elements modulo $p$ in non-commutative Iwasawa theory |
| topic | Number Theory |
| url | https://arxiv.org/abs/2412.13812 |