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

Rössler, D

24 November 2013

## Journal:

Algebra and Number Theory

## Last Updated:

2021-10-09T19:45:13.073+01:00

8

7

## DOI:

10.2140/ant.2013.7.2039

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.

745036

Submitted

Journal Article