Duality for arithmetic Dijkgraaf-Witten theory
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866908504690786304 |
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| author | Eichler, Jaro |
| author_facet | Eichler, Jaro |
| contents | Naidu classified pairs of finite groups and 3-cocycles that lead to equivalent Dijkgraaf-Witten theories for 3-manifolds. We establish analogous equivalences for arithmetic Dijkgraaf-Witten theory over totally imaginary number fields F containing n-th roots of unity, where n is invertible on X subset spec O_F. For the full ring of integers X = spec O_F, we give examples with quadratic fields and the quaternion group Q_8 where these equivalences fail, but also identify sufficient conditions under which they still hold. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_19214 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Duality for arithmetic Dijkgraaf-Witten theory Eichler, Jaro Number Theory Naidu classified pairs of finite groups and 3-cocycles that lead to equivalent Dijkgraaf-Witten theories for 3-manifolds. We establish analogous equivalences for arithmetic Dijkgraaf-Witten theory over totally imaginary number fields F containing n-th roots of unity, where n is invertible on X subset spec O_F. For the full ring of integers X = spec O_F, we give examples with quadratic fields and the quaternion group Q_8 where these equivalences fail, but also identify sufficient conditions under which they still hold. |
| title | Duality for arithmetic Dijkgraaf-Witten theory |
| topic | Number Theory |
| url | https://arxiv.org/abs/2508.19214 |