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The derived homogeneous Fourier transform

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arxiv 2311.13270 v2 pith:24DD4P3O submitted 2023-11-22 math.AG

Adeel A. Khan This is my paper · ORCID
classification math.AG
keywords derivedfouriertransformhomogeneousbundlecontextdualduality
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We study a derived version of Laumon's homogeneous Fourier transform, which exchanges G_m-equivariant sheaves on a derived vector bundle and its dual. In this context, the Fourier transform exhibits a duality between derived and stacky phenomena. This is the first in a series of papers on derived microlocal sheaf theory.

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  1. Modularity of Higher Theta Series III: Proof of the Modularity Conjecture

    math.NT 2026-08 conditional novelty 8.0 of 10

    The higher theta series on Hermitian shtukas are shown to be modular, independent of the chosen Lagrangian, with a stronger supermodularity result for general linear groups.

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