On the Moduli Description of Local Models for Ramified Unitary Groups

Abstract

Local models are schemes which are intended to model the étale-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 toward 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 |$(n-1,1)$|⁠.