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

In this paper, we establish the relation between the Ekedahl-Kottwitz-Oort-Rapoport stratification and the Bruhat-Tits stratification on the unramified $\mathrm{GU}(1,n-1)$ Rapoport-Zink space with arbitrary parahoric level.

More precisely, we prove that every basic EKOR stratum is a disjoint union of copies of a fine Deligne-Lusztig variety which is explicitly defined.

As a consequence, we also 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.