Wildly ramified unitary local models for special parahorics. The odd dimensional case

2024/06/24 by Jie Yang, Yang, Jie · 1 citation
Decision Sciences · #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #demographic modeling and climate adaptation

paper · pdf · doi:10.48550/arxiv.2406.16774

openalex publication_date 2024/06/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

We construct local models for wildly ramified unitary similitude groups of odd dimension n≥ 3 with special parahoric level structure and signature (n-1,1). We first give a lattice-theoretic description for parahoric subgroups using Bruhat-Tits theory in residue characteristic two, and apply them to define local models following the lead of Rapoport-Zink and Pappas-Rapoport. In our case, there are two conjugacy classes of special parahoric subgroups. We show that the local models are smooth for the one class and normal, Cohen-Macaulay for the other class. We also prove that they represent the v-sheaf local models of Scholze-Weinstein. Under some additional assumptions, we obtain an explicit moduli interpretation of the local models.

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