  By means of the theory of strongly semistable sheaves and of the theory of
the Greenberg transform, we generalize to higher dimensions a result on the
sparsity of p-divisible unramified liftings which played a crucial role in
Raynaud's proof of the Manin-Mumford conjecture for curves. We also give a
bound for the number of irreducible components of the first critical scheme of
subvarieties of an abelian variety which are complete intersections.
