On the moduli description of local models for ramified unitary groups

TL;DR

This paper refines the moduli problem for local models of ramified unitary groups, providing a precise characterization in a specific maximal parahoric case with signature (n-1,1).

Contribution

It introduces a necessary and sufficient refinement to the moduli problem for flat local models of ramified unitary groups in a special case.

Findings

Refined the moduli description for local models of ramified unitary groups.

Achieved a complete characterization in the maximal parahoric case with signature (n-1,1).

Enhanced understanding of the explicit moduli problem in this setting.

Abstract

Local models are schemes which are intended to model the \'etale-local structure of p-adic integral models of Shimura varieties. Pappas and Zhu have recently given a general group-theoretic construction of flat local models with parahoric level structure for any tamely ramified group, but it remains an interesting problem to characterize the local models, when possible, in terms of an explicit moduli problem. In the setting of local models for ramified, quasi-split GU_n, work towards an explicit moduli description was initiated in the general framework of Rapoport and Zink's book and was subsequently advanced by Pappas and Pappas-Rapoport. In this paper we propose a further refinement to their moduli problem, which we show is both necessary and sufficient to characterize the (flat) local model in a certain special maximal parahoric case with signature (n-1,1).