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
Mathematical Subject Classification 2010
Primary: 14K12
Secondary: 14K15
Milestones
Received: 9 March 2017
Revised: 9 November 2017
Accepted: 19 December 2017
Published: 13 May 2018
Authors
Danny Scarponi
Fakultät für Mathematik
Universität Regensburg
Germany