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Proof of the geometric Langlands conjecture II: Kac-Moody localization and the FLE

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arxiv 2405.03648 v3 pith:RVSWPIGT submitted 2024-05-06 math.AG

D. Arinkin , D. Beraldo , J. Campbell , L. Chen , J. Faergeman , D. Gaitsgory , K. Lin , S. Raskin
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N. Rozenblyum
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classification math.AG
keywords geometriclanglandsconjecturedevelopmentgoalskac-moodylocalizationprove
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This paper is the second in a series of five that together prove the geometric Langlands conjecture. Our goals are two-fold: (1) Formulate and prove the Fundamental Local Equivalence (FLE) at the critical level; (2) Study the interaction between Kac-Moody localization and the global geometric Langlands functor of ref. [GLC1]. This paper contains an extensive Appendix, whose primary goals are: (a) Development the theory of ind-coherent sheaves in infinite type; (b)Development of the formalism of factorization categories.

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Cited by 6 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. A proof of Dolbeault geometric Langlands for $\mathrm{GL}_2$ with reduced spectral curves

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    For GL_2, the Dolbeault geometric Langlands equivalence is proved over the reduced-spectral-curve locus of the Hitchin base, using limit categories, the Arinkin sheaf, and Wilson/Hecke compatibility.

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    Limit categories are defined, proven compactly generated and semiorthogonally decomposed into quasi-BPS categories, then proposed as the correct automorphic side of the Dolbeault geometric Langlands conjecture.

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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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