On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic

Rössler, Damian

doi:10.2140/ant.2013.7.2039

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On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic

Damian Rössler

Vol. 7 (2013), No. 8, 2039–2057

DOI: 10.2140/ant.2013.7.2039

Abstract

We prove that in positive characteristic, the Manin–Mumford conjecture implies the Mordell–Lang conjecture in the situation where the ambient variety is an abelian variety defined over the function field of a smooth curve over a finite field and the relevant group is a finitely generated group. In particular, in the setting of the last sentence, we provide a proof of the Mordell–Lang conjecture that does not depend on tools coming from model theory.

Keywords

function fields, rational points, positive characteristic, Manin–Mumford, Mordell–Lang

Mathematical Subject Classification 2010

Primary: 14G05

Secondary: 14K12, 14G17

Milestones

Received: 16 July 2012

Revised: 26 October 2012

Accepted: 23 November 2012

Published: 24 November 2013

Authors

Damian Rössler
Institut de Mathématiques, Equipe Emile Picard Université Paul Sabatier 118 Route de Narbonne 31062 Toulouse cedex 9 France
http://www.math.univ-toulouse.fr/~rossler

Vol. 7, No. 8, 2013