### Group Schemes over artinian rings and Applications

Let $n$ be a positive integer and ${A}^{\prime}$ a complete characteristic zero discrete valuation ring with maximal ideal $\U0001d52a$, absolute ramification index $e\<p-1$ and perfect residue field $k$ of characteristic $p\>2$. In this paper we classify smooth finite dimensional formal $p$- groups over ${A}_{n}^{\prime}={A}^{\prime}/{\U0001d52a}^{n}{A}^{\prime}$, groups on which the “multiplication by $p$” morphism is faithfully flat, in particular $p$-divisible groups. As applications, we prove that $p$-divisible groups over $k$, and the morphisms between them, lift canonically to ${A}^{\prime}/p{A}^{\prime}$, and we study liftings...