Open Access
2013 On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic
Damian Rössler
Algebra Number Theory 7(8): 2039-2057 (2013). DOI: 10.2140/ant.2013.7.2039


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.


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Damian Rössler. "On the Manin–Mumford and Mordell–Lang conjectures in positive characteristic." Algebra Number Theory 7 (8) 2039 - 2057, 2013.


Received: 16 July 2012; Revised: 26 October 2012; Accepted: 23 November 2012; Published: 2013
First available in Project Euclid: 20 December 2017

zbMATH: 1295.14024
MathSciNet: MR3134042
Digital Object Identifier: 10.2140/ant.2013.7.2039

Primary: 14G05
Secondary: 14G17 , 14K12

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

Rights: Copyright © 2013 Mathematical Sciences Publishers

Vol.7 • No. 8 • 2013
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