(G, \mu)-displays and Rapoport-Zink spaces

TL;DR

This paper introduces (G, )-displays, generalizing Witt vector displays, to define Rapoport-Zink formal schemes purely group-theoretically, bypassing the need for p-divisible groups.

Contribution

It develops a new group-theoretic framework for Rapoport-Zink spaces using (G, )-displays, extending previous approaches.

Findings

(G, )-displays generalize Witt vector displays.

Rapoport-Zink spaces can be constructed without p-divisible groups.

The approach is purely group-theoretic.

Abstract

Let (G, \mu) be a pair of a reductive group G over the p-adic integers and a minuscule cocharacter {\mu} of G defined over an unramified extension. We introduce and study "(G, \mu)-displays" which generalize Zink's Witt vector displays. We use these to define certain Rapoport-Zink formal schemes purely group theoretically, i.e. without p-divisible groups.