Dieudonné Theory via Prismatic F-gauges

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 generalisation of the work of Anschütz--Le Bras on "prismatic Dieudonne theory" to torsion situations.