Forms on Berkovich spaces based on harmonic tropicalizations
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arXiv
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| Auteurs principaux: | , , |
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| Format: | Preprint |
| Publié: |
2021
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| _version_ | 1866917947462647808 |
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| author | Gubler, Walter Jell, Philipp Rabinoff, Joseph |
| author_facet | Gubler, Walter Jell, Philipp Rabinoff, Joseph |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2111_05741 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Forms on Berkovich spaces based on harmonic tropicalizations Gubler, Walter Jell, Philipp Rabinoff, Joseph Algebraic Geometry Number Theory 14G40 (Primary) 31C05, 32P05, 32U05 (Secondary) 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. |
| title | Forms on Berkovich spaces based on harmonic tropicalizations |
| topic | Algebraic Geometry Number Theory 14G40 (Primary) 31C05, 32P05, 32U05 (Secondary) |
| url | https://arxiv.org/abs/2111.05741 |