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arXiv · 1104.4311

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

Damian Rössler
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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, which does not depend on tools coming from model theory.

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Damian Rössler. 2011-04-21. On the Manin-Mumford and Mordell-Lang conjectures in positive characteristic. https://arxiv.org/abs/1104.4311

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