A tropical formula for non-Archimedean local heights
Algebraic Geometry
2025-12-09 v1 Number Theory
Abstract
We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for . These delta-forms will be used to define the star-product with Green functions of piecewise smooth type on a tropical toric variety. As an application, we show that non-archimedean local heights of projective varieties can be computed using the star-product on a suitable complete tropical toric variety. On the way, we show that open subsets of a simplicial tropical toric variety have a locally finite simplicial decomposition which is constant towards the boundary.
Keywords
Cite
@article{arxiv.2512.07431,
title = {A tropical formula for non-Archimedean local heights},
author = {José Ignacio Burgos Gil and Walter Gubler and Klaus Künnemann},
journal= {arXiv preprint arXiv:2512.07431},
year = {2025}
}