A recent result by the authors gives an explicit construction for a universal deformation of a formal group φ of finite height over a finite field k. This provides in particular a parametrization of the set of deformations of φ over the ring O of Witt vectors over k. Another parametrization of the same set can be obtained through the Dieudonné theory. We find an explicit relation between these parameterizations. As a consequence, we obtain an explicit expression for the action of Autk(φ) on the set of O-deformations of φ in the coordinate system defined by the universal deformation. This generalizes a formula of Gross and Hopkins and the authors' result for one-dimensional formal groups.
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