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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.02002 |
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| _version_ | 1866913008272277504 |
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| author | Souanef, Rafik |
| author_facet | Souanef, Rafik |
| contents | Let $\mathbf{Was}(\mathbb{K})$ denote the group of Washington's cyclotomic units of any abelian number field $\mathbb{K}$. If $\mathbb{K}$ coincides with its genus field in the narrow sense, we give a $Λ$-basis of $\lim\limits\_{\xleftarrow{}} \mathbf{Was}(\mathbb{K}\_k^{+})$ where $(\mathbb{K}\_k)\_{k \geqslant 0}$ denotes the cyclotomic $\mathbb{Z}\_p$-tower of $\mathbb{K}$ and $Λ$ denotes the Iwasawa's algebra. This results from a $\mathbb{Z} [1/2]$-basis of $\mathbf{Was}(\mathbb{K}) \otimes\_{\mathbb{Z}} \mathbb{Z} [1/2]$ that we give under the same hypothesis. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02002 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Bases for some modules of cyclotomic units Souanef, Rafik Number Theory Let $\mathbf{Was}(\mathbb{K})$ denote the group of Washington's cyclotomic units of any abelian number field $\mathbb{K}$. If $\mathbb{K}$ coincides with its genus field in the narrow sense, we give a $Λ$-basis of $\lim\limits\_{\xleftarrow{}} \mathbf{Was}(\mathbb{K}\_k^{+})$ where $(\mathbb{K}\_k)\_{k \geqslant 0}$ denotes the cyclotomic $\mathbb{Z}\_p$-tower of $\mathbb{K}$ and $Λ$ denotes the Iwasawa's algebra. This results from a $\mathbb{Z} [1/2]$-basis of $\mathbf{Was}(\mathbb{K}) \otimes\_{\mathbb{Z}} \mathbb{Z} [1/2]$ that we give under the same hypothesis. |
| title | Bases for some modules of cyclotomic units |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.02002 |