{"paper":{"title":"On the Noncommutative Bondal-Orlov Conjecture","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Michael Wemyss, Osamu Iyama","submitted_at":"2011-01-19T08:35:05Z","abstract_excerpt":"Let R be a normal, equi-codimensional Cohen-Macaulay ring of dimension $d\\geq 2$ with a canonical module. We give a sufficient criterion that establishes a derived equivalence between the noncommutative crepant resolutions of R. When $d\\leq 3$ this criterion is always satisfied and so all noncommutative crepant resolutions of R are derived equivalent. Our method is based on cluster tilting theory for commutative algebras, developed in [IW10]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.3642","kind":"arxiv","version":1},"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"}