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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2306.10227 |
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| _version_ | 1866913539562668032 |
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| author | Goldfarb, Alan |
| author_facet | Goldfarb, Alan |
| contents | We determine the relationship between $\mathbb{C}_p^\times \times \mathbb{C}_p$ and a Berkovich space via an equivalence relation obtained by coarse-graining. This process also establishes a correspondence between $p$-adic fields and Bruhat-Tits trees. From this space, we give a previously unknown construction of the Berkovich projective line $\mathbb{P}_\text{Berk}^1$ and outline a direction for the development of a comprehensive theory of non-Archimedean AdS/CFT and consequently, adelic AdS/CFT, enabled by this construction. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2306_10227 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $\mathbb{P}_{Berk}^1$ and Coarse-Grainings of Non-Archimedean Product Spaces Goldfarb, Alan Number Theory High Energy Physics - Theory Mathematical Physics We determine the relationship between $\mathbb{C}_p^\times \times \mathbb{C}_p$ and a Berkovich space via an equivalence relation obtained by coarse-graining. This process also establishes a correspondence between $p$-adic fields and Bruhat-Tits trees. From this space, we give a previously unknown construction of the Berkovich projective line $\mathbb{P}_\text{Berk}^1$ and outline a direction for the development of a comprehensive theory of non-Archimedean AdS/CFT and consequently, adelic AdS/CFT, enabled by this construction. |
| title | On $\mathbb{P}_{Berk}^1$ and Coarse-Grainings of Non-Archimedean Product Spaces |
| topic | Number Theory High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2306.10227 |