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

Scarponi, Danny

doi:10.2140/ant.2018.12.411

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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

DOI: 10.2140/ant.2018.12.411

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

Vol. 12, No. 2, 2018