Canonical local heights and Berkovich skeleta
Number Theory
2024-05-29 v1 Algebraic Geometry
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.
Keywords
Cite
@article{arxiv.2405.17826,
title = {Canonical local heights and Berkovich skeleta},
author = {Robin de Jong and Farbod Shokrieh},
journal= {arXiv preprint arXiv:2405.17826},
year = {2024}
}