Moduli spaces of analytic p-divisible groups

Abstract: We prove a classification of families of analytic p-divisible groups on adic spaces S over Qp in terms of Hodge–Tate triples on S, generalizing a theorem of Fargues. From this, for S a perfectoid space, we construct an analytic Dieudonné theory with values in mixed characteristic Shtukas over the Fargues–Fontaine disc. As applications, we realize the local Shimura varieties of EL and PEL type of Scholze--Weinstein as moduli spaces of analytic p-divisible groups with framed universal cover, and we reinterpret the Hodge–Tate period map of Scholze in terms of topologically p-torsion subgroups of abelian varieties.