{"paper":{"title":"Proof of the geometric Langlands conjecture IV: ambidexterity","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AG","authors_text":"D. Arinkin, D. Beraldo, D. Gaitsgory, J. Faergeman, K. Lin, L. Chen, N. Rozenblyum, S. Raskin","submitted_at":"2024-09-13T09:35:05Z","abstract_excerpt":"This paper performs the following steps toward the proof of GLC in the de Rham setting:\n  (i) We deduce GLC for G=GL_n;\n  (ii) We prove that the Langlands functor L_G constructed in [GLC1], when restricted to the cuspidal category, is ambidextrous;\n  (iii) We reduce GLC to the study of a certain classical vector bundle with connection on the stack of irreducible local systems;\n  (iv) We prove that GLC is equivalent to the contractibility of the space of generic oper structures on irreducible local systems;\n  (v) Using [BKS], we deduce GLC for classical groups."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.08670","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/2409.08670/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"}