Appears in collection : Journées de géométrie arithmétique de l'IHÉS

This is joint work with Andreas Langer. Let $R$ be an artinian local ring with perfect residue class field $k$. We define Hyper-Kähler manifolds $X$ and their Beauville-Bogomolov form over $R$. We give a lifting criterion in the spirit of Grothendieck and Messing. Over the small Witt ring $\hat{W}(R)$ we associate a 2-display to $X$. If $X$ is ordinary and $S\rightarrow R$ is a surjection of artinian local rings we show that lifting $X$ to $S$ is the same as lifting the 2-display of $X$.