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

Author: 

Rössler, D

Publication Date: 

24 November 2013

Journal: 

Algebra and Number Theory

Last Updated: 

2020-05-21T21:32:21.953+01:00

Issue: 

8

Volume: 

7

DOI: 

10.2140/ant.2013.7.2039

page: 

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.

Symplectic id: 

745036

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article