Jell, Philipp (2016) Real-valued differential forms on Berkovich analytic spaces and their cohomology. PhD, Universität Regensburg.
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Abstract (English)
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.
Translation of the abstract (German)
Wir studieren Superformen auf tropischen Varietäten und Differentialformen auf Berkovichräumen.
Für Superformen auf tropischen Varietäten erweitern wir die bisherigen Definitionen, beweisen ein Poincarélemma und beweisen Poincarédualität für tropische Mannigfaltigkeiten.
Für Differentialformen auf Berkovichräumen beweisen wir ein Poincarélemma und Ergebnisse zur endliche Dimensonalität. Darüber hinaus definieren wir neue, jedoch äquivalente, Zugänge zu Differentialformen auf Berkovichräumen.
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| Item type: | Thesis of the University of Regensburg (PhD) |
|---|---|
| Date: | 2 October 2016 |
| Referee: | Prof. Dr. Klaus Künnemann |
| Date of exam: | 27 October 2016 |
| Institutions: | Mathematics > Prof. Dr. Klaus Künnemann Mathematics > Prof. Dr. Walter Gubler |
| Keywords: | Superforms, Berkovich spaces, Tropical variety, Tropical geometry, Poincaré Lemma |
| Dewey Decimal Classification: | 500 Science > 510 Mathematics |
| Status: | Published |
| Refereed: | Yes, this version has been refereed |
| Created at the University of Regensburg: | Yes |
| Item ID: | 34788 |
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