{"paper":{"title":"Finiteness and dimension of stated skein modules over Frobenius","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"Zhihao Wang","submitted_at":"2023-09-19T20:34:49Z","abstract_excerpt":"When the quantum parameter $q^{1/2}$ is a root of unity of odd order. The stated skein module $S_{q^{1/2}}(M,\\mathcal{N})$ has an $S_{1}(M,\\mathcal{N})$-module structure, where $(M,\\mathcal{N})$ is a marked three manifold. We prove $S_{q^{1/2}}(M,\\mathcal{N})$ is a finitely generated $S_{1}(M,\\mathcal{N})$-module when $M$ is compact, which furthermore indicates the reduced stated skein module for the compact marked three manifold is finite dimensional. We also give an upper bound for the dimension of $S_{q^{1/2}}(M,\\mathcal{N})$ over $S_{1}(M,\\mathcal{N})$ when $M$ is compact.\n  For a pb surfa"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.10920","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/2309.10920/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"}