{"paper":{"title":"Stratifications of derived categories from tilting modules over tame hereditary algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA"],"primary_cat":"math.RT","authors_text":"Changchang Xi, Hongxing Chen","submitted_at":"2011-07-03T10:25:10Z","abstract_excerpt":"In this paper, we consider the endomorphism algebras of infinitely generated tilting modules of the form $R_{\\mathcal U}\\oplus R_{\\mathcal U}/R$ over tame hereditary $k$-algebras $R$ with $k$ an arbitrary field, where $R_{\\mathcal{U}}$ is the universal localization of $R$ at an arbitrary set $\\mathcal{U}$ of simple regular $R$-modules, and show that the derived module category of $\\End_R(R_{\\mathcal U}\\oplus R_{\\mathcal U}/R)$ is a recollement of the derived module category $\\D{R}$ of $R$ and the derived module category $\\D{{\\mathbb A}_{\\mathcal{U}}}$ of the ad\\`ele ring ${\\mathbb A}_{\\mathcal"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1107.0444","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"}