{"paper":{"title":"Cohomology of Jacobi forms","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.NT","authors_text":"A. Zuevsky","submitted_at":"2021-06-11T06:45:51Z","abstract_excerpt":"We define and study a cohomology theory for the space of Jacobi $n$-point functions generated by a vertex operator (super)algebra, using precise analogues of Zhu's reduction formulas. A cochain complex $(C^{\\bullet}(W), \\delta^{\\bullet})$ is constructed whose coboundary operators are given by Zhu-type reduction maps, and whose cohomology groups $H^{n}_{J}(W)$ we call the {reduction cohomology of Jacobi forms}. We prove that the $n$-th reduction cohomology of a $V$-module $W$ is isomorphic to the space of analytic continuations of solutions to a vertex-operator-algebraic analogue of the Knizhni"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2106.07773","kind":"arxiv","version":7},"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/2106.07773/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"}