In this talk, I will first describe how classical Dieudonne module of finite flat group schemes and p-divisible groups can be recovered from crystalline cohomology of classifying stacks. Then, I will explain how in mixed characteristics, using classifying stacks, one can define Dieudonné module of a finite locally free group scheme as a prismatic F-gauge (prismatic F-gauges have been recently introduced by Drinfeld and Bhatt-Lurie), which gives a fully faithful functor from finite locally free group schemes over a quasi-syntomic algebra to the category of prismatic F-gauges. This can be seen as a generalization of the work of Anschütz-Le Bras on “prismatic Dieudonne theory” to torsion situations.
This video is part of the Institute for Advanced Study‘s Special year seminar 2023/24.
