The Basic Locus of the Unitary Shimura Variety With Minuscule Parahoric Level Structure, and Special Cycles

In this paper, we study the basic locus in the fibre at p of a certain unitary Shimura variety with a certain parahoric level structure. The basic locus M s s ^ Mˢˢ ModifyingAbove script upper M Superscript s s Baseline With caret is uniformized by a formal scheme N N script upper N , which is called the Rapoport–Zink space. We show that the irreducible components of the induced reduced subscheme N r e d Nred script upper N Subscript r e d of N N script upper N are Deligne–Lusztig varieties and their intersection behaviour is controlled by a certain Bruhat-Tits building. Also, we define special cycles in N N script upper N and study their intersection multiplicities.