On the fourth power level of $\mathfrak{p}$-adic completions of biquadratic number fields
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912663362076672 |
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| author | Chomicz, Kazimierz |
| author_facet | Chomicz, Kazimierz |
| contents | Let $K$ be a number field and $\mathfrak{p} \mid (2)$ be a prime ideal. We compute the fourth level of the $\mathfrak{p}$-adic completions of $K$ when the ramification index is $4$ and the inertial degree is trivial for the ideal $\mathfrak{p}$. This enables the computation of the fourth level of any $\mathfrak{p}$-adic completion of any quartic number field. Here we apply this result to biquadratic number fields and obtain lower bounds for the fourth level of such number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_21559 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On the fourth power level of $\mathfrak{p}$-adic completions of biquadratic number fields Chomicz, Kazimierz Number Theory Let $K$ be a number field and $\mathfrak{p} \mid (2)$ be a prime ideal. We compute the fourth level of the $\mathfrak{p}$-adic completions of $K$ when the ramification index is $4$ and the inertial degree is trivial for the ideal $\mathfrak{p}$. This enables the computation of the fourth level of any $\mathfrak{p}$-adic completion of any quartic number field. Here we apply this result to biquadratic number fields and obtain lower bounds for the fourth level of such number fields. |
| title | On the fourth power level of $\mathfrak{p}$-adic completions of biquadratic number fields |
| topic | Number Theory |
| url | https://arxiv.org/abs/2503.21559 |