Dieudonn\'e Theory via Cohomology of Classifying Stacks.
2020
We prove that if $G$ is a finite flat group scheme or a $p$-divisible group, then the second crystalline cohomology of its classifying stack $H^2_{crys}(BG)$ recovers the Dieudonne module of $G$. We also prove mixed characteristic analogues of this result using prismatic cohomology.
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