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arXiv · 2409.08670

Proof of the geometric Langlands conjecture IV: ambidexterity

D. Arinkin·D. Beraldo·L. Chen·J. Faergeman·D. Gaitsgory·K. Lin·S. Raskin·N. Rozenblyum
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Abstract

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.

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D. Arinkin, D. Beraldo, L. Chen, J. Faergeman, D. Gaitsgory, K. Lin, S. Raskin, N. Rozenblyum. 2024-09-13. Proof of the geometric Langlands conjecture IV: ambidexterity. https://arxiv.org/abs/2409.08670

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