Prismatic Dieudonné theory

Abstract

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

Replaced the notion of filtered prismatic Dieudonné crystal by the equivalent (but simpler) notion of admissible prismatic Dieudonné crystal; corrected and simplified (following a suggestion of Mathew) the proof of fully faithfulness; many small changes