{"paper":{"title":"Shifted Symplectic Structures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AT","math.KT"],"primary_cat":"math.AG","authors_text":"B. Toen, G. Vezzosi, M. Vaquie, T. Pantev","submitted_at":"2011-11-14T13:35:52Z","abstract_excerpt":"This is the first of a series of papers about \\emph{quantization} in the context of \\emph{derived algebraic geometry}. In this first part, we introduce the notion of \\emph{$n$-shifted symplectic structures}, a generalization of the notion of symplectic structures on smooth varieties and schemes, meaningful in the setting of derived Artin n-stacks. We prove that classifying stacks of reductive groups, as well as the derived stack of perfect complexes, carry canonical 2-shifted symplectic structures. Our main existence theorem states that for any derived Artin stack $F$ equipped with an $n$-shif"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.3209","kind":"arxiv","version":4},"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"}