D. Arinkin, D. Beraldo, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin, N. Rozenblyum
{"title":"几何朗兰兹猜想的证明IV：伏羲性","authors":"D. Arinkin, D. Beraldo, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin, N. Rozenblyum","doi":"arxiv-2409.08670","DOIUrl":null,"url":null,"abstract":"This paper performs the following steps toward the proof of GLC in the de\nRham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [GLC1], when\nrestricted to the cuspidal category, is ambidextrous; (iii) We reduce GLC to the study of a certain classical vector bundle with\nconnection on the stack of irreducible local systems; (iv) We prove that GLC is equivalent to the contractibility of the space of\ngeneric oper structures on irreducible local systems; (v) Using [BKS], we deduce GLC for classical groups.","PeriodicalId":501063,"journal":{"name":"arXiv - MATH - Algebraic Geometry","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Proof of the geometric Langlands conjecture IV: ambidexterity\",\"authors\":\"D. Arinkin, D. Beraldo, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin, N. Rozenblyum\",\"doi\":\"arxiv-2409.08670\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper performs the following steps toward the proof of GLC in the de\\nRham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [GLC1], when\\nrestricted to the cuspidal category, is ambidextrous; (iii) We reduce GLC to the study of a certain classical vector bundle with\\nconnection on the stack of irreducible local systems; (iv) We prove that GLC is equivalent to the contractibility of the space of\\ngeneric oper structures on irreducible local systems; (v) Using [BKS], we deduce GLC for classical groups.\",\"PeriodicalId\":501063,\"journal\":{\"name\":\"arXiv - MATH - Algebraic Geometry\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"arXiv - MATH - Algebraic Geometry\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/arxiv-2409.08670\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"arXiv - MATH - Algebraic Geometry","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/arxiv-2409.08670","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Proof of the geometric Langlands conjecture IV: ambidexterity
This paper performs the following steps toward the proof of GLC in the de
Rham setting: (i) We deduce GLC for G=GL_n; (ii) We prove that the Langlands functor L_G constructed in [GLC1], when
restricted to the cuspidal category, is ambidextrous; (iii) We reduce GLC to the study of a certain classical vector bundle with
connection on the stack of irreducible local systems; (iv) We prove that GLC is equivalent to the contractibility of the space of
generic oper structures on irreducible local systems; (v) Using [BKS], we deduce GLC for classical groups.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
