{"paper":{"title":"Relative singularity categories, Gorenstein objects and silting theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AC","math.AG","math.CT","math.RA"],"primary_cat":"math.RT","authors_text":"Jiaqun Wei","submitted_at":"2015-04-25T15:15:31Z","abstract_excerpt":"We study singularity categories through Gorenstein objects in triangulated categories and silting theory. Let ${\\omega}$ be a semi-selforthogonal (or presilting) subcategory of a triangulated category $\\mathcal{T}$. We introduce the notion of $\\omega$-Gorenstein objects, which is far extended version of Gorenstein projective modules and Gorenstein injective modules in triangulated categories. We prove that the stable category $\\underline{\\mathcal{G}_{\\omega}}$, where $\\mathcal{G}_{\\omega}$ is the subcategory of all ${\\omega}$-Gorenstein objects, is a triangulated category and it is, under some"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.06738","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"}