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

TL;DR

This paper provides a detailed description of Rapoport--Zink spaces for spinor groups with special maximal parahoric level structure, and explores applications to Shimura varieties and intersection multiplicities.

Contribution

It offers a concrete description of the reduced subscheme of these Rapoport--Zink spaces and applies this to study basic loci of Shimura varieties and intersection formulas.

Findings

Explicit description of the reduced subscheme of Rapoport--Zink spaces

Analysis of the structure of basic loci in mod p reductions of Shimura varieties

A formula for intersection multiplicities of GGP cycles

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 non-hyperspecial) 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.