Prismatic Dieudonné theory

Johannes Anschütz , Arthur-César Le Bras (1, 2)

1 LAGA - Laboratoire Analyse, Géométrie et Applications
2 IRMA - Institut de Recherche Mathématique Avancée

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

Domaines: Mathématiques [math]

Johannes Anschütz, Arthur-César Le Bras. Prismatic Dieudonné theory. Forum of Mathematics, Pi, 2023, 11 (e2). ⟨hal-03018452v2⟩