Forms on Berkovich spaces based on harmonic tropicalizations

arXiv (Cornell University)(2021)

Cited 0|Views1
No score
Abstract
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-Archimedean field. Chambert-Loir and Ducros introduced bigraded sheaves of smooth real-valued differential forms on Berkovich spaces by pulling back Lagerberg forms with respect to tropicalization maps. We give a new approach in which we allow pullback by more general harmonic tropicalizations to get a larger sheaf of differential forms with essentially the same properties, but with a better cohomological behavior. A crucial ingredient is that tropical varieties arising from harmonic tropicalization maps are balanced.
More
Translated text
Key words
berkovich spaces
AI Read Science
Must-Reading Tree
Example
Generate MRT to find the research sequence of this paper
Chat Paper
Summary is being generated by the instructions you defined