On parahoric $(\mathcal{G},\mu )$-displays

Abstract

We develop tools to study spaces of $p$-divisible groups and Abelian varieties with additional structure. More precisely, we extend the definition of parahoric (Dieudonné) $(\mathcal{G},\mu )$-displays given by Pappas to not necessarily $p$-torsionfree base rings and also introduce the notion of an $(m,n)$-truncated $(\mathcal{G},\mu )$-display. Then we study the deformation theory of Dieudonné $(\mathcal{G},\mu )$-displays. As an application we realize the EKOR stratification of the special fiber of a Kisin-Pappas integral Shimura variety of Hodge type as the fibers of a smooth morphism into the algebraic stack of $(2,1\text{-}\mathrm{rdt})$-truncated $(\mathcal{G},\mu )$-displays.

37 pages