{"paper":{"title":"The Dolbeault geometric Langlands correspondence for type A groups beyond the elliptic locus","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Yukinobu Toda","submitted_at":"2026-06-27T11:44:57Z","abstract_excerpt":"In this paper, we prove a Dolbeault geometric Langlands equivalence for $\\GL_r$ and for the Langlands dual pair $\\SL_r/\\PGL_r$ over an open locus of the Hitchin base which strictly contains the elliptic locus. This open locus contains the points corresponding to spectral curves with at worst type $A$ singularities, without any restriction on the number of irreducible components.\n  The Dolbeault geometric Langlands equivalence considered here is the one formulated in our previous work with Tudor P\\u{a}durariu, which links categorical Donaldson--Thomas theory with the geometric Langlands corresp"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.28878","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/2606.28878/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"}