The cyclosyntomic regulator of a number field
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866910032878108672 |
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| author | Bouis, Tess Gazda, Quentin |
| author_facet | Bouis, Tess Gazda, Quentin |
| contents | We construct a q-deformation of the p-adic regulator of a number field, called the cyclosyntomic regulator, building on the Habiro ring of Garoufalidis-Scholze-Wheeler-Zagier. The key new ingredient in our construction is a refinement of Sulyma's norm maps in prismatic cohomology, which interpolate between classical powers and Frobenius maps at various prime numbers p. Furthermore, we compute the values of the cyclosyntomic regulator at units of the form $1-ζ$, where $ζ$ is a root of unity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_21894 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The cyclosyntomic regulator of a number field Bouis, Tess Gazda, Quentin Number Theory Algebraic Geometry K-Theory and Homology 19F27, 05A30, 11G55 We construct a q-deformation of the p-adic regulator of a number field, called the cyclosyntomic regulator, building on the Habiro ring of Garoufalidis-Scholze-Wheeler-Zagier. The key new ingredient in our construction is a refinement of Sulyma's norm maps in prismatic cohomology, which interpolate between classical powers and Frobenius maps at various prime numbers p. Furthermore, we compute the values of the cyclosyntomic regulator at units of the form $1-ζ$, where $ζ$ is a root of unity. |
| title | The cyclosyntomic regulator of a number field |
| topic | Number Theory Algebraic Geometry K-Theory and Homology 19F27, 05A30, 11G55 |
| url | https://arxiv.org/abs/2602.21894 |