{"paper":{"title":"Frobenius homomorphisms for stated ${\\rm SL}_n$-skein modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.GT","authors_text":"Hyun Kyu Kim, Thang T. Q. L\\^e, Zhihao Wang","submitted_at":"2025-04-11T15:59:50Z","abstract_excerpt":"The stated ${\\rm SL}_n$-skein algebra $\\mathscr{S}_{\\hat{q}}(\\mathfrak{S})$ of a surface $\\mathfrak{S}$ is a quantization of the ${\\rm SL}_n$-character variety, and is spanned over $\\mathbb{Z}[\\hat{q}^{\\pm 1}]$ by framed tangles in $\\mathfrak{S} \\times (-1,1)$. If $\\hat{q}$ is evaluated at a root of unity $\\hat{\\omega}$ with the order of $\\hat{\\omega}^{4n^2}$ being $N$, then for $\\hat{\\eta} = \\hat{\\omega}^{N^2}$, the Frobenius homomorphism $\\Phi : \\mathscr{S}_{\\hat{\\eta}}(\\mathfrak{S}) \\to \\mathscr{S}_{\\hat{\\omega}}(\\mathfrak{S})$ is a surface generalization of the well-known Frobenius homomor"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2504.08657","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/2504.08657/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"}