Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866908454503841792 |
|---|---|
| author | Ozaki, Manabu |
| author_facet | Ozaki, Manabu |
| contents | For any finite cyclic $p$-group $G$, we will show that every $\mathbb{Z}_p$-torsion free finitely generated $\mathbb{Z}_p[G]$-module appears as $\mathcal{O}_K^\times\otimes_{\mathbb{Z}}\mathbb{Z}_p$ up to $\mathbb{Z}_p[G]$-free direct summands for a certain $G$-extension $K/k$ of number fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_12949 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure Ozaki, Manabu Number Theory For any finite cyclic $p$-group $G$, we will show that every $\mathbb{Z}_p$-torsion free finitely generated $\mathbb{Z}_p[G]$-module appears as $\mathcal{O}_K^\times\otimes_{\mathbb{Z}}\mathbb{Z}_p$ up to $\mathbb{Z}_p[G]$-free direct summands for a certain $G$-extension $K/k$ of number fields. |
| title | Construction of a cyclic $p$-extension of number fields whose unit group has prescribed Galois module structure |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.12949 |