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| Main Authors: | , , , , , , , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2409.08670 |
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| _version_ | 1866913499179909120 |
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| author | Arinkin, D. Beraldo, D. Chen, L. Faergeman, J. Gaitsgory, D. Lin, K. Raskin, S. Rozenblyum, N. |
| author_facet | Arinkin, D. Beraldo, D. Chen, L. Faergeman, J. Gaitsgory, D. Lin, K. Raskin, S. Rozenblyum, N. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_08670 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Proof of the geometric Langlands conjecture IV: ambidexterity Arinkin, D. Beraldo, D. Chen, L. Faergeman, J. Gaitsgory, D. Lin, K. Raskin, S. Rozenblyum, N. Algebraic Geometry 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. |
| title | Proof of the geometric Langlands conjecture IV: ambidexterity |
| topic | Algebraic Geometry |
| url | https://arxiv.org/abs/2409.08670 |