The Arinkin-Gaitsgory temperedness conjecture

2021/08/05 by Joakim Færgeman, Faergeman, Joakim, Sam Raskin +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2108.02719

openalex publication_date 2021/08/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Arinkin and Gaitsgory defined a category of tempered D-modules on Bun_G that is conjecturally equivalent to the category of quasi-coherent (not ind-coherent!) sheaves on LocSys_\checkG. However, their definition depends on the auxiliary data of a point of the curve; they conjectured that their definition is independent of this choice. Beraldo has outlined a proof of this conjecture that depends on some technology that is not currently available. Here we provide a short, unconditional proof of the Arinkin-Gaitsgory conjecture.

Citations

• Outline of the proof of the geometric Langlands conjecture for GL(2)

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