$\delta$-Forms on Lubin--Tate Space

TL;DR

This paper generalizes the theory of $ abla$-forms to Berkovich spaces, linking formal models, Green currents, and intersection theory, with applications to Lubin--Tate spaces.

Contribution

It extends $ abla$-forms to Berkovich spaces and connects intersection numbers with $ abla$-product of Green currents, broadening divisor intersection results.

Findings

Complete intersection formal models produce Green $ abla$-forms.

Intersection numbers are given by the $ abla$-product of Green currents.

Application to intersection problems in Lubin--Tate spaces.

Abstract

We extend Gubler--K\"unnemann's theory of $\delta$-forms from algebraic varieties to good Berkovich spaces. This is based on the observation that skeletons in such spaces satisfy a tropical balance condition. Our main result is that complete intersection formal models of cycles give rise to Green $\delta$-forms for their generic fibers. We moreover show that, in certain situations, intersection numbers on formal models are given by the $\star$-product of their Green currents. In this way, we generalize some results for divisor intersection to higher codimension situations. We illustrate the mentioned results in the context of an intersection problem for Lubin--Tate spaces.