Unramified Iwasawa module of $\mathbb{Z}_2$-extension of certain quadratic fields with a bounded quotient
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866914744154193920 |
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| author | Laxmi, H Saikia, Anupam |
| author_facet | Laxmi, H Saikia, Anupam |
| contents | We consider an infinite family of real quadratic fields $k$ where the discriminant has three distinct odd prime factors, and the prime 2 splits. We show that the unramified Iwasawa module $X(k_{\infty})$ associated with the $\mathbb{Z}_2$-extension of $k$ has a bounded quotient. Thus, we also verify Greenberg's conjecture on the vanishing of Iwasawa invariants for such fields and obtain a finer structure for $X(k_{\infty})$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_05190 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Unramified Iwasawa module of $\mathbb{Z}_2$-extension of certain quadratic fields with a bounded quotient Laxmi, H Saikia, Anupam Number Theory 11R29, 11R11, 11R23 We consider an infinite family of real quadratic fields $k$ where the discriminant has three distinct odd prime factors, and the prime 2 splits. We show that the unramified Iwasawa module $X(k_{\infty})$ associated with the $\mathbb{Z}_2$-extension of $k$ has a bounded quotient. Thus, we also verify Greenberg's conjecture on the vanishing of Iwasawa invariants for such fields and obtain a finer structure for $X(k_{\infty})$. |
| title | Unramified Iwasawa module of $\mathbb{Z}_2$-extension of certain quadratic fields with a bounded quotient |
| topic | Number Theory 11R29, 11R11, 11R23 |
| url | https://arxiv.org/abs/2404.05190 |