Arithmetic subgroups of Chevalley group schemes over function fields II: Conjugacy classes of maximal unipotent subgroups

2023/07/20 by Claudio Bravo, Bravo, Claudio, Benoît Loisel +1
Mathematics · Medicine · #20E42 (secondary) #20E45 (primary) 11R58 #20G30 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Group Theory (math.GR) #Magnolia and Illicium research #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2307.11193

openalex publication_date 2023/07/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth, projective, geometrically integral curve defined over a perfect field \mathbbF. Let k=\mathbbF(C) be the function field of C. Let G be a split simply connected semisimple ℤ-group scheme. Let S be a finite set of places of C. In this paper, we investigate on the conjugacy classes of maximal unipotent subgroups of S-arithmetic subgroups. These are parameterized thanks to the Picard group of O_S and the rank of G. Furthermore, these maximal unipotent subgroups can be realized as the unipotent part of natural stabilizer, which are the stabilizers of sectors of the associated Bruhat-Tits building. We decompose these natural stabilizers in terms of their diagonalisable part and unipotent part, and we precise the group structure of the diagonalisable part.

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