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Derived structures in the Langlands Correspondence

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arxiv 2409.03035 v2 pith:R4BFOJJC submitted 2024-09-04 math.NT math.AGmath.RT

Tony Feng , Michael Harris This is my paper · ORCID
classification math.NTmath.AGmath.RT
keywords derivedcorrespondencelanglandsstructuresalgebrascasesconnectioncycles
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We survey several recent examples of derived structures emerging in connection with the Langlands correspondence. Cases studies include derived Galois deformation rings, derived Hecke algebras, derived Hitchin stacks, and derived special cycles. We also highlight some open problems that we expect to be important for future progress.

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  1. Spectral moduli problems for level structures and an integral Jacquet-Langlands dual of Morava E-theory

    math.AT 2025-08 conditional novelty 7.0 of 10

    Derived level structures in spectral algebraic geometry are representable, yielding Jacquet-Langlands spectra and a proposed Jacquet-Langlands dual of Morava E-theory.

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