{"paper":{"title":"A Poincar\\'e lemma for real-valued differential forms on Berkovich spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Philipp Jell","submitted_at":"2014-09-02T11:59:24Z","abstract_excerpt":"Real-valued differential forms on Berkovich analytic spaces were introduced by Chambert-Loir and Ducros in 'Formes diff\\'erentielles r\\'eelles et courants sur les espaces de Berkovich' using superforms on polyhedral complexes. We prove a Poincar\\'e lemma for these superforms and use it to also prove a Poincar\\'e 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 analyti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.0676","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}