Prismatic Dieudonne theory

We define, for each quasi-syntomic ring $R$ (in the sense of Bhatt-Morrow-Scholze), a category $mathrm{DF}(R)$ of textit{filtered prismatic Dieudonne crystals over $R$} and a natural functor from $p$-divisible groups over $R$ to $mathrm{DF}(R)$. We prove that this functor is an antiequivalence. Our main cohomological tool is the prismatic formalism recently developed by Bhatt and Scholze.