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arXiv · 2405.17826

Canonical local heights and Berkovich skeleta

Robin de Jong·Farbod Shokrieh
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Abstract

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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Robin de Jong, Farbod Shokrieh. 2024-05-28. Canonical local heights and Berkovich skeleta. https://arxiv.org/abs/2405.17826

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