{"paper":{"title":"Appoximate Cohomology","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO","math.DS"],"primary_cat":"math.GR","authors_text":"David Kazhdan, Tamar Ziegler","submitted_at":"2017-02-04T17:19:13Z","abstract_excerpt":"Let $k$ be a field, $G$ be an abelian group and $r\\in \\mathbb N$. Let $L$ be an infinite dimensional $k$-vector space. For any $m\\in End_k(L)$ we denote by $r(m)\\in [0,\\infty ]$ the rank of $m$. We define by $R(G,r,k)\\in [0,\\infty]$ the minimal $R$ such that for any map $A:G \\to End_k(L)$ with $r(A(g'+g'')-A(g')-A(g''))\\leq r$, $g',g''\\in G$ there exists a homomorphism $\\chi :G\\to End_k(L)$ such that $r(A(g)-\\chi (g))\\leq R(G, r, k)$ for all $g\\in G$. We show the finiteness of $R(G,r,k)$ for the case when $k$ is a finite field, $G=V$ is a $k$-vector space $V$ of countable dimension. We actuall"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1702.01308","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"}