The wavefront set over a maximal unramified field extension

2021/07/22 by Emile Takahiro Okada, Okada, Emile
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.2107.10591

openalex publication_date 2021/07/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let (π,X) be a depth-0 admissible smooth complex representation of a p-adic reductive group that splits over an unramified extension. In this paper we develop the theory necessary to study the wavefront set of X over a maximal unramified field extension of the base p-adic field. In the final section we then apply these methods to compute the geometric wavefront set of spherical Arthur representations of split p-adic reductive groups. In this case we see how the wavefront set over a maximal unramified extension can be computed using perverse sheaves on the Langlands dual group.

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