The Bruhat-Tits stratification for basic unramified $GU(1,n-1)$ Rapoport-Zink spaces at arbitrary parahoric level

Abstract

In this paper, we describe a stratification on the reduced special fiber of the basic unramified unitary Rapoport-Zink space of signature $(1,n-1)$ and at arbitrary parahoric level. We prove the smoothness, irreducibility and compute the dimensions of the closed strata, which are isomorphic to the closure of certain fine Deligne-Lusztig varieties for a product of unitary and general linear groups. We also describe the incidence relations of the stratification by using Bruhat-Tits indices, which are related to the Bruhat-Tits building of an underlying $p$-adic unitary group.