Rapoport-Zink spaces for spinor groups

TL;DR

This paper develops a theory of Rapoport-Zink formal schemes for Hodge type Shimura varieties and applies it to spinor groups, explicitly describing the underlying reduced schemes in basic cases.

Contribution

It introduces a new framework for Hodge type Rapoport-Zink spaces and explicitly characterizes the reduced schemes for spinor group cases.

Findings

Established a theory for Hodge type Rapoport-Zink formal schemes.

Explicit description of reduced schemes for spinor group cases.

Unified approach to uniformizing Shimura varieties at good primes.

Abstract

We develop a theory of Hodge type Rapoport-Zink formal schemes, which uniformize certain formal completions of the canonical integral models of Shimura varieties of Hodge type at primes of good reduction. We then apply the general theory to the special case of Shimura varieties associated with groups of spinor similitudes, and, in the basic case, determine explicitly the reduced scheme underlying the Rapoport-Zink formal scheme.