Canonical subgroups of formal groups

Abstract

Let R be a complete local domain of mixed characteristic. This paper gives a complete answer to the question: “If F is a one-dimensional formal group over R of finite height, when is there a canonical morphism F → F ′ F \to {F’} that lifts Frobenius?” For given height h, a universal family of formal groups F with such a morphism is constructed, and the shape of F ′ {F’} is described for small values of h.