Divided Dieudonné crystals

Abstract

Abstract We define a category of divided Dieudonné crystals which classifies 𝑝-divisible groups over schemes in characteristic 𝑝 with certain finiteness conditions, including all 𝐹-finite noetherian schemes. For formally smooth schemes or locally complete intersections, this generalizes and extends known results on the classical crystalline Dieudonné functor.