| Résume | We prove a classification of analytic $p$-divisible groups over perfectoid spaces $S$ over $\mathbb{Q}_p$ in terms of Hodge--Tate triples on $S$, generalizing a theorem of Fargues. From this, we construct an analytic Dieudonné theory with values in mixed characteristic Shtukas over the Fargues--Fontaine disc. We use our results to realize the local Shimura varieties of EL and PEL type of Scholze--Weinstein as moduli spaces of analytic $p$-divisible groups, and we reinterpret the Hodge--Tate period map of Scholze in terms of $p$-topological torsion subgroups of abelian varieties. |
