δ-Forms on Lubin–Tate spaces

We extend Gubler and Künnemann’s theory of δ-forms from algebraic varieties to good Berkovich spaces. This is based on the observation that skeletons in such spaces satisfy a tropical balancing condition. Our first theorem in this formalism is a construction of Green’s δ-forms for complete intersection cycles. Our second theorem is a formula for Artinian intersection numbers on formal models in terms of integrals of δ-forms on their generic fibers. These two results generalize known results from divisors to higher codimension. Finally, we illustrate our intersection number formula in the context of an intersection problem for Lubin–Tate spaces.