  Generalizing the Moret-Bailly pencil of supersingular abelian surfaces to
higher dimensions, we construct for each field of characteristic p>0 a smooth
projective variety with trivial dualizing sheaf that does not formally lift to
characteristic zero. Our approach heavily relies on local unipotent group
schemes, the Beauville--Bogomolov Decomposition for K\"ahler manifolds with
$c_1=0$, and equivariant deformation theory
