{"paper":{"title":"Arithmetic-Geometric Correspondence of Character Stacks via Topological Quantum Field Theory","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.CT","math.MP","math.RT"],"primary_cat":"math.AG","authors_text":"\\'Angel Gonz\\'alez-Prieto, Jesse Vogel, M\\'arton Hablicsek","submitted_at":"2023-09-27T00:27:46Z","abstract_excerpt":"In this paper, we introduce Topological Quantum Field Theories (TQFTs) generalizing the arithmetic computations done by Hausel and Rodr\\'iguez-Villegas and the geometric construction done by Logares, Mu\\~noz, and Newstead to study cohomological invariants of $G$-representation varieties and $G$-character stacks. We show that these TQFTs are related via a natural transformation that we call the 'arithmetic-geometric correspondence' generalizing the classical formula of Frobenius on the irreducible characters of a finite group. We use this correspondence to extract some information on the charac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2309.15331","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/2309.15331/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"}