We report on proofs of some recent conjectures of Drinfeld on the algebraicity of formal stacks associated with minuscule cocharacters of smooth group schemes over Z_p. These stacks are constructed using the theory of syntomification as developed by Bhatt-Lurie and Drinfeld, and yield an essentially linear algebraic window to the world of p-divisible groups, generalizing classical Dieudonne theory. This is joint work with Zachary Gardner and Akhil Mathew.