The geometry of the unipotent component of the moduli space of Weil–Deligne representations

Funck, Daniel

doi:10.2140/ant.2026.20.1125

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The geometry of the unipotent component of the moduli space of Weil–Deligne representations

Daniel Funck

Vol. 20 (2026), No. 6, 1125–1158

DOI: 10.2140/ant.2026.20.1125

Abstract

We study the moduli space of unipotent Weil–Deligne representations valued in a split reductive group $G$ and characterise which irreducible components are smooth. We apply these smoothness results to show that a certain space of ordinary automorphic forms is a locally generically free module over the corresponding global deformation ring.

Keywords

number theory, moduli space of Langlands parameters, Galois representation, patching, automorphic form

Mathematical Subject Classification

Primary: 11F70, 11F80

Secondary: 11F33

Milestones

Received: 24 July 2023

Revised: 25 March 2025

Accepted: 27 June 2025

Published: 26 May 2026

Authors

Daniel Funck
University of Tübingen 72076 Tüebingen Germany

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Vol. 20, No. 6, 2026