On the Finiteness and Structure of Galois Groups of Tamely ramified pro-p Extensions of Imaginary Quadratic Fields
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866911149442727936 |
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| author | Liu, Qi Xing, Zugan |
| author_facet | Liu, Qi Xing, Zugan |
| contents | For a prime p, we study the Galois groups of maximal pro-$p$ extensions of imaginary quadratic fields unramified outside a finite set $S$, where $S$ consists of one or two finite places not lying above $p$. When $p$ is odd, we give explicit presentations of these Galois groups under certain conditions. As an application, we determine the structure of the maximal pro-$3$ extension of $\mathbb{Q}(i)$ unramified outside two specific finite places. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2411_03155 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Finiteness and Structure of Galois Groups of Tamely ramified pro-p Extensions of Imaginary Quadratic Fields Liu, Qi Xing, Zugan Number Theory 11R32, 11R37, 12F10, 11R11, 20D15 For a prime p, we study the Galois groups of maximal pro-$p$ extensions of imaginary quadratic fields unramified outside a finite set $S$, where $S$ consists of one or two finite places not lying above $p$. When $p$ is odd, we give explicit presentations of these Galois groups under certain conditions. As an application, we determine the structure of the maximal pro-$3$ extension of $\mathbb{Q}(i)$ unramified outside two specific finite places. |
| title | On the Finiteness and Structure of Galois Groups of Tamely ramified pro-p Extensions of Imaginary Quadratic Fields |
| topic | Number Theory 11R32, 11R37, 12F10, 11R11, 20D15 |
| url | https://arxiv.org/abs/2411.03155 |