An afterthought on the generalized Mordell-Lang conjecture
Number Theory
2007-05-23 v1 Algebraic Geometry
Abstract
The generalized Mordell-Lang conjecture (GML) is the statement that the irreducible components of the Zariski closure of a subset of a group of finite rank inside a semi-abelian variety are translates of closed algebraic subgroups. M. McQuillan gave a proof of this statement. We revisit his proof, indicating some simplifications. This text contains a complete elementary proof of the fact that (GML) for groups of torsion points (= generalized Manin-Mumford conjecture), together with (GML) for finitely generated groups imply the full generalized Mordell-Lang conjecture.
Cite
@article{arxiv.math/0510408,
title = {An afterthought on the generalized Mordell-Lang conjecture},
author = {Damian Rossler},
journal= {arXiv preprint arXiv:math/0510408},
year = {2007}
}