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On $\mathbb{P}_{Berk}^1$ and Coarse-Grainings of Non-Archimedean Product Spaces (2306.10227v2)
Published 17 Jun 2023 in math.NT, hep-th, math-ph, and math.MP
Abstract: 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.