{"paper":{"title":"A Gabriel Theorem for Coherent Twisted Sheaves","license":"","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Arvid Perego","submitted_at":"2006-07-01T17:08:24Z","abstract_excerpt":"We give a generalization of Gabriel's Theorem on coherent sheaves to the case of coherent twisted sheaves on a smooth variety X over a field k. We show that the category Coh(X,\\alpha) determines the scheme structure of X for \\alpha in the Brauer group of X, and that any equivalence between Coh(X,\\alpha) and Coh(Y,\\beta) induces an isomorphism between X and Y. In conclusion we prove the saturatedness of D^b(X,\\alpha)."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0607025","kind":"arxiv","version":2},"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"}