{"paper":{"title":"A generalized Bondal-Orlov full faithfulness criterion for Deligne-Mumford stacks","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Jack Hall, Kyle Priver","submitted_at":"2024-05-10T03:48:45Z","abstract_excerpt":"Let $X$, $Y$ be smooth projective varieties over $\\mathbf{C}$. Let $K$ be a bounded complex of coherent sheaves on $X\\times Y$ and let $\\Phi_K \\colon \\mathsf{D}^b_{\\mathsf{Coh}}(X) \\to \\mathsf{D}^b_{\\mathsf{Coh}}(Y)$ be the resulting Fourier-Mukai functor. There is a well-known criterion due to Bondal-Orlov for $\\Phi_K$ to be fully faithful. This criterion was recently extended to smooth Deligne-Mumford stacks with projective coarse moduli schemes by Lim-Polischuk. We extend this to all smooth, proper Deligne-Mumford stacks over arbitrary fields of characteristic $0$. Along the way, we establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2405.06229","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2405.06229/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}