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

TL;DR

This paper extends the understanding of p-divisible unramified liftings for subvarieties of abelian varieties, providing new bounds and generalizations using advanced sheaf and transform theories.

Contribution

It generalizes a key result on the sparsity of p-divisible liftings to higher dimensions and establishes bounds on the irreducible components of critical schemes.

Findings

Generalized sparsity results for p-divisible unramified liftings in higher dimensions.

Provided bounds for the number of irreducible components of critical schemes.

Extended techniques to analyze subvarieties of abelian varieties.

Abstract

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.