{"paper":{"title":"A remark on $\\mathbb{T}$-valued cohomology groups of algebraic group actions","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.DS","math.GR"],"primary_cat":"math.OA","authors_text":"Yongle Jiang","submitted_at":"2015-09-28T11:25:11Z","abstract_excerpt":"We prove that for a weakly mixing algebraic action $\\sigma: G\\curvearrowright(X,\\nu)$, the $n$-cohomology group $H^n(G\\curvearrowright X; \\mathbb{T})$, after quotienting out the natural subgroup $H^n(G,\\mathbb{T})$, contains $H^n(G,\\widehat{X})$ as a natural subgroup for $n=1$. If we further assume the diagonal actions $\\sigma^2, \\sigma^4$ are $\\mathbb{T}$-cocycle superrigid and $H^2(G, \\widehat{X})$ is torsion free as an abelian group, then the above also holds true for $n=2$. Applying it for principal algebraic actions when $n=1$, we show that $H^2(G,\\mathbb{Z}G)$ is torsion free as an abeli"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.08278","kind":"arxiv","version":2},"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"}