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arXiv · 2512.07431

A tropical formula for non-Archimedean local heights

José Ignacio Burgos Gil·Walter Gubler·Klaus Künnemann
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Abstract

We introduce delta-forms on tropical toric varieties generalizing the construction of Mihatsch for $R^n$. 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.

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José Ignacio Burgos Gil, Walter Gubler, Klaus Künnemann. 2025-12-08. A tropical formula for non-Archimedean local heights. https://arxiv.org/abs/2512.07431

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