{"paper":{"title":"Derived Recollements and Generalised AR Formulas","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Jeremy Russell, Samuel Dean","submitted_at":"2016-12-06T03:14:44Z","abstract_excerpt":"The Defect Recollement, Restriction Recollement, Auslander-Gruson-Jensen Recollement, and others, are shown to be instances of a general construction using derived functors and methods from stable module theory. The right derived functors $\\textsf{W}_k:=R_k(\\hspace{0.05cm}\\underline{\\ \\ }\\hspace{0.1cm} )^*$ are computed and it is shown that the functor $\\textsf{W}_2:=R_2(\\hspace{0.05cm}\\underline{\\ \\ }\\hspace{0.1cm} )^*$ is right exact and restricts to a duality $\\textsf{W}$ of the defect zero functors. The duality $\\textsf{W}$ satisfies two identities which we call the Generalised Auslander-R"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1612.01651","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"}