{"paper":{"title":"A Derived Legendrian Category for Shifted Contact Stacks","license":"http://creativecommons.org/licenses/by/4.0/","headline":"The derived Legendrian category F_c(X) is constructed for any n-shifted contact derived Artin stack X using Legendrian correspondences.","cross_cats":["math.SG"],"primary_cat":"math.AG","authors_text":"Efe \\.Izbudak, Kadri \\.Ilker Berktav","submitted_at":"2026-05-13T17:12:35Z","abstract_excerpt":"We construct the derived Legendrian category $\\mathcal{F}_{c}(X)$ for an $n$-shifted contact derived Artin stack $X$ and the $(\\infty,2)$-category $Leg_n$ of Legendrian correspondences in the context of derived algebraic geometry, with several applications to moduli theory. In brief, the objects of the category $\\mathcal{F}_{c}(X)$ are Legendrian morphisms; the morphism spaces and composition operations are defined using equivariant descent. We also establish that $\\mathcal{F}_{c}(X)$ embeds into an $(\\infty, 2)$-category of spans defined by the AKSZ construction. We further evaluate topologic"},"claims":{"count":4,"items":[{"kind":"strongest_claim","text":"We construct the derived Legendrian category F_c(X) for an n-shifted contact derived Artin stack X and the (∞,2)-category Leg_n of Legendrian correspondences... We also establish that F_c(X) embeds into an (∞,2)-category of spans defined by the AKSZ construction. We further evaluate topological cobordisms as Lagrangian correspondences to define derived Legendrian surgery.","source":"verdict.strongest_claim","status":"machine_extracted","claim_id":"C1","attestation":"unclaimed"},{"kind":"weakest_assumption","text":"The existence of n-shifted contact structures on derived Artin stacks X together with the well-definedness of equivariant descent for morphism spaces and composition in the derived setting.","source":"verdict.weakest_assumption","status":"machine_extracted","claim_id":"C2","attestation":"unclaimed"},{"kind":"one_line_summary","text":"A new derived Legendrian category is built for shifted contact stacks in derived algebraic geometry, embedding into span categories and enabling Legendrian surgery.","source":"verdict.one_line_summary","status":"machine_extracted","claim_id":"C3","attestation":"unclaimed"},{"kind":"headline","text":"The derived Legendrian category F_c(X) is constructed for any n-shifted contact derived Artin stack X using Legendrian correspondences.","source":"verdict.pith_extraction.headline","status":"machine_extracted","claim_id":"C4","attestation":"unclaimed"}],"snapshot_sha256":"059a16668dabddf17bb26628c7847a352902feb87c38521a5660bee72b8c2f82"},"source":{"id":"2605.13792","kind":"arxiv","version":1},"verdict":{"id":"19c3b9ee-986e-4a44-ab48-20e9966a704b","model_set":{"reader":"grok-4.3"},"created_at":"2026-05-14T17:42:05.182592Z","strongest_claim":"We construct the derived Legendrian category F_c(X) for an n-shifted contact derived Artin stack X and the (∞,2)-category Leg_n of Legendrian correspondences... We also establish that F_c(X) embeds into an (∞,2)-category of spans defined by the AKSZ construction. We further evaluate topological cobordisms as Lagrangian correspondences to define derived Legendrian surgery.","one_line_summary":"A new derived Legendrian category is built for shifted contact stacks in derived algebraic geometry, embedding into span categories and enabling Legendrian surgery.","pipeline_version":"pith-pipeline@v0.9.0","weakest_assumption":"The existence of n-shifted contact structures on derived Artin stacks X together with the well-definedness of equivariant descent for morphism spaces and composition in the derived setting.","pith_extraction_headline":"The derived Legendrian category F_c(X) is constructed for any n-shifted contact derived Artin stack X using Legendrian correspondences."},"references":{"count":8,"sample":[{"doi":"","year":2026,"title":"Equivariant Quotients of Derived Symplectic Spaces and Legendrian Intersection Theorem","work_id":"31f804d5-5218-4573-ab22-282123a500dd","ref_index":1,"cited_arxiv_id":"2605.08394","is_internal_anchor":true},{"doi":"","year":2013,"title":"T. Pantev, B. To¨en, M. Vaqui´e, G. Vezzosi,Shifted Symplectic Structures, Publ. Math. Inst. Hautes ´Etudes Sci. 117 (2013), 271-328","work_id":"5429ff6a-1ade-4513-b92e-ed8422979ef8","ref_index":2,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2019,"title":"Calaque,Shifted cotangent stacks are shifted symplectic, Ann","work_id":"e5aef04a-869f-4200-8669-13f902beaf0c","ref_index":3,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2022,"title":"D. Calaque, R. Haugseng, C. Scheimbauer,The AKSZ Construction in Derived Algebraic Geometry as an Extended T opological Field Theory, arXiv:2108.02473, 2022","work_id":"14e57951-c1e2-4d80-99c0-1228b0aba387","ref_index":4,"cited_arxiv_id":"","is_internal_anchor":false},{"doi":"","year":2024,"title":"K. ˙I. Berktav,Shifted Contact Structures and Their Local Theory, Ann. Fac. Sci. Toulouse, Math., Serie 6, Vol. 33(4): 1019-1057, 2024","work_id":"0d403f32-de5b-4f27-83a5-5e3fe3762598","ref_index":5,"cited_arxiv_id":"","is_internal_anchor":false}],"resolved_work":8,"snapshot_sha256":"35dc3151169b4bd4b39186097321efe174076d0df762c87713df7058d8458d15","internal_anchors":2},"formal_canon":{"evidence_count":2,"snapshot_sha256":"5048d3e138eb0439a75fde97d620d4408a28773153817fb132d6fb71c53c9ee9"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}