On a bound of $p$-ranks of Iwasawa modules of $\mathbb{Z}_p$-extensions over a quartic CM-field
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arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866909950811308032 |
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| author | Yanagisawa, Takuya |
| author_facet | Yanagisawa, Takuya |
| contents | Let $p$ be a prime number. If a number field $k$ has at least one complex place, there are infinitely many $\mathbb{Z}_p$-extensions over $k$, and some authors studied the behavior of Iwasawa invariants of these $\mathbb{Z}_p$-extensions. In particular, Fujii studied the case where $k$ is an imaginary quadratic field and obtained some results on the boundedness of Iwasawa $λ$-invariants in a certain infinite family of $\mathbb{Z}_p$-extensions. In the present article, we give analogous theorems in the case where $k$ is a quartic CM-field. One of our main theorems determines all the Iwasawa invariants, including the $ν$-invariants, of a certain infinite family of $\mathbb{Z}_p$-extensions over a quartic CM-field. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_08278 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a bound of $p$-ranks of Iwasawa modules of $\mathbb{Z}_p$-extensions over a quartic CM-field Yanagisawa, Takuya Number Theory Let $p$ be a prime number. If a number field $k$ has at least one complex place, there are infinitely many $\mathbb{Z}_p$-extensions over $k$, and some authors studied the behavior of Iwasawa invariants of these $\mathbb{Z}_p$-extensions. In particular, Fujii studied the case where $k$ is an imaginary quadratic field and obtained some results on the boundedness of Iwasawa $λ$-invariants in a certain infinite family of $\mathbb{Z}_p$-extensions. In the present article, we give analogous theorems in the case where $k$ is a quartic CM-field. One of our main theorems determines all the Iwasawa invariants, including the $ν$-invariants, of a certain infinite family of $\mathbb{Z}_p$-extensions over a quartic CM-field. |
| title | On a bound of $p$-ranks of Iwasawa modules of $\mathbb{Z}_p$-extensions over a quartic CM-field |
| topic | Number Theory |
| url | https://arxiv.org/abs/2512.08278 |