Class number behavior in a two-tiered tower of $\mathbb{Z}_p$-extensions
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866912046948286464 |
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| author | Itoh, Tsuyoshi |
| author_facet | Itoh, Tsuyoshi |
| contents | Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension field of an algebraic number field $k$. Moreover, we take a $\mathbb{Z}_p$-extension $K_\infty$ over $k_\infty$. In this paper, we study the behavior of the $p$-part of the class number of certain intermediate fields of $K_\infty /k$. We also consider the structure of the unramified Iwasawa module of $K_\infty / k_\infty$ for several cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_19751 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Class number behavior in a two-tiered tower of $\mathbb{Z}_p$-extensions Itoh, Tsuyoshi Number Theory 11R23 Let $k_\infty$ be the cyclotomic $\mathbb{Z}_p$-extension field of an algebraic number field $k$. Moreover, we take a $\mathbb{Z}_p$-extension $K_\infty$ over $k_\infty$. In this paper, we study the behavior of the $p$-part of the class number of certain intermediate fields of $K_\infty /k$. We also consider the structure of the unramified Iwasawa module of $K_\infty / k_\infty$ for several cases. |
| title | Class number behavior in a two-tiered tower of $\mathbb{Z}_p$-extensions |
| topic | Number Theory 11R23 |
| url | https://arxiv.org/abs/2407.19751 |