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

By Damian Rössler

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.Comment: arXiv admin note: substantial text overlap with arXiv:1103.262

Topics: Mathematics - Algebraic Geometry, Mathematics - Logic, Mathematics - Number Theory, 14K12
Year: 2012
OAI identifier: oai:arXiv.org:1104.4311
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