Real-valued differential forms on Berkovich analytic spaces and their cohomology
Philipp Jell · University of Regensburg Publication Server (University of Regensburg) · 2016
We study superforms on tropical varieties and differential forms on Berkovich spaces. For superforms on tropical varieties, we extend the previous defintionts, prove a Poincaré lemma and prove Poincaré duality for tropical manifolds. For differential forms on Berkovich spaces we also prove a Poincaré lemma and finite dimensionality results. We further define new, but equivalent, approaches to differential forms on Berkovich spaces.