#### Vol. 12, No. 2, 2018

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

### Danny Scarponi

Vol. 12 (2018), No. 2, 411–428
##### 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.

##### Keywords
Manin–Mumford conjecture, number fields, $p$-divisible unramified liftings, Greenberg transform, strongly semistable sheaves
Primary: 14K12
Secondary: 14K15