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| Format: | Preprint |
| Publié: |
2025
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2507.05693 |
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| _version_ | 1866916885256208384 |
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| author | Uramoto, Takeo |
| author_facet | Uramoto, Takeo |
| contents | Following Cornelissen, Li, Marcolli, and Smit, this short paper proves that the field structure of a number field $K$ can be reconstructed from the pair $(DR_K, I_K)$ of the Deligne-Ribet monoid $DR_K$ and the submonoid $I_K$ of $DR_K$, when $K$ is the rational number field, or an imaginary quadratic field. The general-case reconstruction is also discussed, which is more abstract than the case of rational and imaginary quadratic fields. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_05693 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Absolute reconstruction of number fields from the Deligne-Ribet monoids Uramoto, Takeo Number Theory Following Cornelissen, Li, Marcolli, and Smit, this short paper proves that the field structure of a number field $K$ can be reconstructed from the pair $(DR_K, I_K)$ of the Deligne-Ribet monoid $DR_K$ and the submonoid $I_K$ of $DR_K$, when $K$ is the rational number field, or an imaginary quadratic field. The general-case reconstruction is also discussed, which is more abstract than the case of rational and imaginary quadratic fields. |
| title | Absolute reconstruction of number fields from the Deligne-Ribet monoids |
| topic | Number Theory |
| url | https://arxiv.org/abs/2507.05693 |