Vol. 7, No. 8, 2013

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

Damian Rössler

Vol. 7 (2013), No. 8, 2039–2057
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