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Proof of the geometric Langlands conjecture IV: ambidexterity

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arxiv 2409.08670 v1 pith:ETNRZVXL submitted 2024-09-13 math.AG

D. Arinkin , D. Beraldo , L. Chen , J. Faergeman , D. Gaitsgory , K. Lin , S. Raskin , N. Rozenblyum This is my paper · ORCID
classification math.AG
keywords classicaldeduceirreduciblelanglandslocalproofprovesystems
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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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Cited by 3 Pith papers

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    For any adjoint reductive group at rational Kac-Moody level, cuspidal twisted D-modules with nilpotent singular support have at least one nonzero quantum Whittaker coefficient, proved microlocally.

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