{"paper":{"title":"Annihilation of cohomology and decompositions of derived categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Ryo Takahashi, Srikanth B. Iyengar","submitted_at":"2014-05-21T05:07:03Z","abstract_excerpt":"It is proved that an element $r$ in the center of a coherent ring $\\Lambda$ annihilates $\\mathrm{Ext}^{n}_{\\Lambda}(M,N)$, for some positive integer $n$ and all finitely presented $\\Lambda$-modules $M$ and $N$, if and only if the bounded derived category of $\\Lambda$ is an extension of the subcategory consisting of complexes annihilated by $r$ and those obtained as $n$-fold extensions of $\\Lambda$. This has applications to finiteness of dimension of derived categories."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.5299","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"}