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

2011/04/21 by Rössler, Damian · 1 citation
#14K12 #Algebraic Geometry (math.AG) #FOS: Mathematics #Logic (math.LO) #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1104.4311

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.

Cited by

• Adelic Mordell-Lang and the Brauer-Manin obstruction

Related

• Around the Mordell-Lang and Manin-Mumford conjectures in positive characteristic
• A positive characteristic Manin–Mumford theorem
• Positive characteristic Manin-Mumford theorem
• Mordell-Lang in positive characteristic
• A sparsity result for the Dynamical Mordell-Lang Conjecture in positive characteristic