Rapoport--Zink spaces for spinor groups with special maximal parahoric level structure

Abstract

In this article, we give a concrete description of the underlying reduced subscheme of the Rapoport-Zink spaces for spinor similitude groups with special maximal parahoric (and nonhyperspecial) level structure. Moreover, we give two applications of the above result. One of which is describing the structure of the basic loci of mod p reductions of Kisin-Pappas integral models of Shimura varieties for spinor similitude groups with special maximal parahoric level structure at p. The other is constructing a variant of the result of He, Li and Zhu, which gives a formula on the intersection multiplicity of the GGP cycles associated codimension 1 embeddings of Rapoport-Zink spaces for spinor similitude groups.