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math.AG2021
Dolbeault Cohomology of Graphs and Berkovich Curves
Walter Gubler, Philipp Jell, Joseph Rabinoff
We introduce real-valued -forms on weighted metric graphs with boundary similar to Lagerberg forms on polyhedral spaces. We compute the Dolbeault cohomology and prove Poinca…
math.AG2021
Forms on Berkovich spaces based on harmonic tropicalizations
Walter Gubler, Philipp Jell, Joseph Rabinoff
We introduce tropical skeletons for Berkovich spaces based on results of Ducros. Then we study harmonic functions on good strictly analytic spaces over a non-trivially valued non-A…