Extremal cases of Rapoport-Zink spaces

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.

Basic loci of Coxeter type with arbitrary parahoric level

“…We use the same labeling of the Coxeter graph as in Bourbaki [2, Plate I-X]. As in [10], we use the following notation for automorphisms of affine Dynkin diagrams. In case the fundamental coweight ω ∨ i is minuscule, we denote the corresponding length 0 element τ (t ω ∨ i ) by τ i ; conjugation by τ i is a length preserving automorphism of W which we denote by Ad(τ i ).…”