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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2407.02063 |
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| _version_ | 1866913567647727616 |
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| author | Kim, Dohyeong Morishita, Masanori |
| author_facet | Kim, Dohyeong Morishita, Masanori |
| contents | Triple symbols are arithmetic analogues of the mod $n$ triple linking number in topology, where $n > 1$ is an integer. In this paper, we introduce a cohomological formulation of a mod $n$ triple symbol for characters over a number field containing a primitive $n$-th root of unity. Our definition is motivated by the arithmetic Chern--Simons theory and in this respect it differs from earlier approaches to triple symbols. We show that our symbol agrees with that of Rédei when $n=2$ and of Amano--Mizusawa--Morishita when $n=3$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_02063 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Triple symbols in arithmetic Kim, Dohyeong Morishita, Masanori Number Theory Triple symbols are arithmetic analogues of the mod $n$ triple linking number in topology, where $n > 1$ is an integer. In this paper, we introduce a cohomological formulation of a mod $n$ triple symbol for characters over a number field containing a primitive $n$-th root of unity. Our definition is motivated by the arithmetic Chern--Simons theory and in this respect it differs from earlier approaches to triple symbols. We show that our symbol agrees with that of Rédei when $n=2$ and of Amano--Mizusawa--Morishita when $n=3$. |
| title | Triple symbols in arithmetic |
| topic | Number Theory |
| url | https://arxiv.org/abs/2407.02063 |