On the basic locus of GSpin Shimura varieties with vertex stabilizer level

TL;DR

This paper investigates the structure of the basic locus in GSpin Shimura varieties with vertex stabilizer level, providing a detailed description of the associated Rapoport--Zink space's reduced scheme, extending previous results.

Contribution

It generalizes existing descriptions of Rapoport--Zink spaces for GSpin Shimura varieties to cases with self-dual and almost self-dual level structures.

Findings

Description of the reduced scheme of Rapoport--Zink space

Extension of Howard--Pappas and Oki's results

Applicable to self-dual and almost self-dual level structures

Abstract

We study the basic locus of Shimura varieties associated to the group of spinor similitudes of a quadratic space over $\mathbb{Q}$ with level structure given by the stabilizer of a vertex lattice. We give a description of the underlying reduced scheme of the associated Rapoport--Zink space, generalizing results of Howard--Pappas [HP17] and Oki [Oki20b], in the case of self-dual, and almost self dual level structure.