Canonical local heights and Berkovich skeleta

Farbod Shokrieh; Robin de Jong

Canonical local heights and Berkovich skeleta

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arxiv 2405.17826 v1 pith:XWGYCSTW submitted 2024-05-28 math.NT math.AG

Robin de Jong , Farbod Shokrieh This is my paper · ORCID

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keywords canonicalheightslocaleronberkovichformulasresulttate

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We discuss canonical local heights on abelian varieties over non-archimedean fields from the point of view of Berkovich analytic spaces. Our main result is a refinement of N\'eron's classical result relating canonical local heights with intersection multiplicities on the N\'eron model. We also revisit Tate's explicit formulas for N\'eron's canonical local heights on elliptic curves. Our results can be viewed as extensions of Tate's formulas to higher dimensions.

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