{"paper":{"title":"Relative Singularity Categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Huanhuan Li, Zhaoyong Huang","submitted_at":"2015-02-09T04:17:42Z","abstract_excerpt":"We study the properties of the relative derived category $D_{\\mathscr{C}}^{b}$($\\mathscr{A}$) of an abelian category $\\mathscr{A}$ relative to a full and additive subcategory $\\mathscr{C}$. In particular, when $\\mathscr{A}=A{\\text -}\\mod$ for a finite-dimensional algebra $A$ over a field and $\\mathscr{C}$ is a contravariantly finite subcategory of $A$-$\\mod$ which is admissible and closed under direct summands, the $\\mathscr{C}$-singularity category $D_{\\mathscr{C}{\\text sg}}$($\\mathscr{A}$)=$D_{\\mathscr{C}}^{b}$($\\mathscr{A}$)/$K^{b}(\\mathscr{C})$ is studied. We give a sufficient condition wh"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1502.02349","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"}