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

Abstract

By means of the theory of strongly semistable sheaves and 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.