As I understand it, both Arakelov geometry and Berkovich geometry over $\Bbb Z$ (or $\mathcal O_K$) consider geometric objects that contain in some sense information about both archimdean and nonarchimedean places. So it seems natural (at least to my naïve mind) to ask if there is any relation between the two approaches.
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4$\begingroup$ Have you checked out Sections 3 and 4 of arxiv.org/pdf/2105.13587.pdf. The authors define a theory of adelic line bundles and integration pairings using Berkovich spaces over $\mathbb{Z}$ and relate this to classical Arakelov intersection pairings. $\endgroup$– Jackson MorrowCommented Sep 30, 2023 at 18:45
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$\begingroup$ @JacksonMorrow thanks for the reference! $\endgroup$– Lukas HegerCommented Oct 7, 2023 at 18:46
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