{"paper":{"title":"On the Ext-computability of Serre quotient categories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AG"],"primary_cat":"math.KT","authors_text":"Markus Lange-Hegermann, Mohamed Barakat","submitted_at":"2012-12-17T16:59:36Z","abstract_excerpt":"To develop a constructive description of $\\mathrm{Ext}$ in categories of coherent sheaves over certain schemes, we establish a binatural isomorphism between the $\\mathrm{Ext}$-groups in Serre quotient categories $\\mathcal{A}/\\mathcal{C}$ and a direct limit of $\\mathrm{Ext}$-groups in the ambient Abelian category $\\mathcal{A}$. For $\\mathrm{Ext}^1$ the isomorphism follows if the thick subcategory $\\mathcal{C} \\subset \\mathcal{A}$ is localizing. For the higher extension groups we need further assumptions on $\\mathcal{C}$. With these categories in mind we cannot assume $\\mathcal{A}/\\mathcal{C}$ t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1212.4068","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"}