On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2020
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| _version_ | 1866911891297665024 |
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| author | Chems-Eddin, Mohamed Mahmoud Zekhnini, Abdelkader Azizi, Abdelmalek |
| author_facet | Chems-Eddin, Mohamed Mahmoud Zekhnini, Abdelkader Azizi, Abdelmalek |
| contents | In this paper, we study the length of the $2$-class field towers and the structure of the Galois groups $\mathrm{Gal}(\mathcal{L}(K_n)/K_n)$ of the maximal unramified $2$-extensions of the layers $K_n$ of the cyclotomic $\mathbb{Z}_2$-extension of some special Dirichlet fields. The capitulation problem is investigated too. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2005_06646 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions Chems-Eddin, Mohamed Mahmoud Zekhnini, Abdelkader Azizi, Abdelmalek Number Theory In this paper, we study the length of the $2$-class field towers and the structure of the Galois groups $\mathrm{Gal}(\mathcal{L}(K_n)/K_n)$ of the maximal unramified $2$-extensions of the layers $K_n$ of the cyclotomic $\mathbb{Z}_2$-extension of some special Dirichlet fields. The capitulation problem is investigated too. |
| title | On the Hilbert $2$-class field towers of some cyclotomic $\mathbb{Z}_2$-extensions |
| topic | Number Theory |
| url | https://arxiv.org/abs/2005.06646 |