THE BASIC LOCUS OF THE UNITARY SHIMURA VARIETY WITH MINUSCULE PARAHORIC LEVEL STRUCTURE, AND SPECIAL CYCLES

Abstract 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 ^ $\widehat {{\mathcal M}^{ss}}$ ModifyingAbove script upper M Superscript s s Baseline With caret is uniformized by a formal scheme N ${\mathcal N}$ 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 ${\mathcal N}_{red}$ script upper N Subscript r e d of N ${\mathcal N}$ 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 ${\mathcal N}$ script upper N and study their intersection multiplicities.