Proof of the geometric Langlands conjecture IV: ambidexterity
Algebraic Geometry
2024-09-16 v1
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.
Keywords
Cite
@article{arxiv.2409.08670,
title = {Proof of the geometric Langlands conjecture IV: ambidexterity},
author = {D. Arinkin and D. Beraldo and L. Chen and J. Faergeman and D. Gaitsgory and K. Lin and S. Raskin and N. Rozenblyum},
journal= {arXiv preprint arXiv:2409.08670},
year = {2024}
}