{"paper":{"title":"Derived sheaves in locally conformally symplectic geometry","license":"http://creativecommons.org/licenses/by-nc-sa/4.0/","headline":"","cross_cats":["math.AT"],"primary_cat":"math.SG","authors_text":"Adrien Currier","submitted_at":"2026-05-18T16:23:45Z","abstract_excerpt":"In this paper, we use derived sheaves to study rigidity phenomena in the cotangent bundles of manifolds endowed with some locally conformally symplectic ($\\frak{lcs}$) structure. Taking inspiration from the work of Guillermou, Kashiwara and Shapira, we define a quantization for ``$\\frak{lcs}$'' Hamiltonian isotopies, as well as new quantities: the asymptotic Betti numbers of a sheaf. We then show that those quantities are ``well behaved'' with respect of said quantization and use this to give a sheaf-theoretical proof of the Chantraine-Murphy theorem. We also consider the quantization in light"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.18614","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/2605.18614/integrity.json","findings":[],"available":true,"detectors_run":[{"name":"claim_evidence","ran_at":"2026-05-20T00:01:59.232380Z","status":"completed","version":"1.0.0","findings_count":0}],"snapshot_sha256":"ca1a60e68fcd24f0d3215d379e40719742d4706e1a09429973d9ccd76c6de448"},"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"}