{"paper":{"title":"A 'Darboux Theorem' for shifted symplectic structures on derived Artin stacks, with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Christopher Brav, Dominic Joyce, Oren Ben-Bassat, Vittoria Bussi","submitted_at":"2013-11-30T11:21:49Z","abstract_excerpt":"This is the fifth in a series arXiv:1304.4508, arXiv:1305,6302, arXiv:1211.3259, arXiv:1305.6428 on the '$k$-shifted symplectic derived algebraic geometry' of Pantev, Toen, Vaquie and Vezzosi, arXiv:1111.3209. This paper extends the previous three from (derived) schemes to (derived) Artin stacks. We prove four main results:\n  (a) If $(X,\\omega)$ is a $k$-shifted symplectic derived Artin stack for $k<0$ in the sense of arXiv:1111.3209, then near each $x\\in X$ we can find a 'minimal' smooth atlas $\\varphi:U\\to X$ with $U$ an affine derived scheme, such that $(U,\\varphi^*(\\omega))$ may be written"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.0090","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1312.0090/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"}