Mathematics, Algebraic Geometry, Algebraic Geometry (math.AG), Number Theory (math.NT)
journal:
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date:
2023-10-30 16:00:00
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 (Dieudonn\'e) $(\mathcal{G}, \mu)$-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 Dieudonn\'e $(\mathcal{G}, \mu)$-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.PDF: On parahoric $(\mathcal{G}, \mu)$-displays.pdf
