EKOR and BT stratifications for basic unramified $\mathrm{GU}(1,n-1)$ Rapoport-Zink spaces

Abstract

In this paper, we establish the relation between the Ekedahl-Kottwitz-Oort-Rapoport stratification and the Bruhat-Tits stratification on basic unramified $\mathrm{GU}(1,n-1)$ Rapoport-Zink spaces with arbitrary parahoric level. More precisely, we prove that every basic EKOR stratum is a disjoint union of copies of an explicitly defined fine Deligne-Lusztig variety. Using this comparison and the closure relations for fine Deligne-Lusztig varieties, we give an explicit combinatorial description of the closure of every basic EKOR stratum. As further applications, we determine which KR strata are entirely contained in the basic locus, and we prove the smoothness of the irreducible components of the closure of certain EKOR strata.

arXiv comment73 pages, important revision: improved the overall exposition and added an elementary description of the closure of the EKOR strata