Prismatic Dieudonné Theory

We define, for each quasisyntomic ring R (in the sense of Bhatt et al., Publ. Math. IHES 129 (2019), 199–310), a category DMᵃᵈᵐ(R) of admissible prismatic Dieudonné crystals over R and a functor from p -divisible groups over R to DMᵃᵈᵐ(R) . We prove that this functor is an antiequivalence. Our main cohomological tool is the prismatic formalism recently developed by Bhatt and Scholze.