Dieudonne theory and cohomology of classifying stack

In this talk, I will first describe how the 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 to classify finite flat group schemes over a fairly general base by using classifying stacks and the formalism of prismatic F-gauges due to Drinfeld and Bhatt--Lurie.