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

Sparsity of p-divisible unramified liftings for subvarieties of abelian varieties with trivial stabilizer