{"paper":{"title":"de Rham and Dolbeault Cohomology of solvmanifolds with local systems","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.DG","authors_text":"Hisashi Kasuya","submitted_at":"2012-07-17T13:38:41Z","abstract_excerpt":"Let $G$ be a simply connected solvable Lie group with a lattice $\\Gamma$ and the Lie algebra $\\g$ and a representation $\\rho:G\\to GL(V_{\\rho})$ whose restriction on the nilradical is unipotent. Consider the flat bundle $E_{\\rho}$ given by $\\rho$. By using \"many\" characters $\\{\\alpha\\}$ of $G$ and \"many\" flat line bundles $\\{E_{\\alpha}\\}$ over $G/\\Gamma$, we show that an isomorphism \\[\\bigoplus_{\\{\\alpha\\}} H^{\\ast}(\\g, V_{\\alpha}\\otimes V_{\\rho})\\cong \\bigoplus_{\\{E_{\\alpha}\\}} H^{\\ast}(G/\\Gamma, E_{\\alpha}\\otimes E_{\\rho})\\] holds. This isomorphism is a generalization of the well-known fact:\""},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1207.3988","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"}