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

2024/05/06 by D. Arinkin, Dario Beraldo, Arinkin, D. +15 · 6 citations
Mathematics · Physics and Astronomy · #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Algebraic Geometry (math.AG) #FOS: Mathematics #Geometry and complex manifolds

paper · pdf · doi:10.48550/arxiv.2405.03648

openalex publication_date 2024/05/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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