Extremal cases of Rapoport-Zink spaces

TL;DR

This paper classifies extremal cases of Rapoport-Zink spaces, focusing on when their underlying schemes have minimal or maximal dimension, with explicit lists for both scenarios.

Contribution

It provides a complete classification of zero-dimensional and maximal-dimensional Rapoport-Zink spaces, highlighting the model cases of Lubin-Tate and Drinfeld moduli spaces.

Findings

Complete list of zero-dimensional Rapoport-Zink spaces

Complete list of maximal-dimensional Rapoport-Zink spaces

Identification of Lubin-Tate and Drinfeld spaces as models

Abstract

We investigate qualitative properties of the underlying scheme of Rapoport-Zink formal moduli spaces of p-divisible groups, resp. Shtukas. We single out those cases when the dimension of this underlying scheme is zero, resp. those where the dimension is maximal possible. The model case for the first alternative is the Lubin-Tate moduli space, and the model case for the second alternative is the Drinfeld moduli space. We exhibit a complete list in both cases.