Jell, Philipp (2016) A Poincar, lemma for real-valued differential forms on Berkovich spaces. MATHEMATISCHE ZEITSCHRIFT, 282 (3-4). pp. 1149-1167. ISSN 0025-5874, 1432-1823
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Real-valued differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros in (Formes diff,rentielles r,elles et courants sur les espaces de Berkovich. arXiv:1204.6277, 2012) using superforms on polyhedral complexes. We prove a Poincar, lemma for these superforms and use it to also prove a Poincar, lemma for real-valued differential forms on Berkovich spaces. For superforms we further show finite dimensionality for the associated de Rham cohomology on polyhedral complexes in all (bi-)degrees. We also show finite dimensionality for the real-valued de Rham cohomology of the analytification of an algebraic variety in some bidegrees.
| Item Type: | Article |
|---|---|
| Uncontrolled Keywords: | ; |
| Subjects: | 500 Science > 510 Mathematics |
| Divisions: | Mathematics |
| Depositing User: | Dr. Gernot Deinzer |
| Date Deposited: | 26 Mar 2019 06:26 |
| Last Modified: | 26 Mar 2019 06:26 |
| URI: | https://pred.uni-regensburg.de/id/eprint/3199 |
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