MathSciDoc: An Archive for Mathematician ∫

Algebraic GeometryNumber Theorymathscidoc:1808.07016

International Mathematics Research Notices, 2011, (22), 5109–5122, 2011
We provide a family of counterexamples to a first formulation of the dynamical Manin–Mumford conjecture. We propose a revision of this conjecture and prove it for arbitrary subvarieties of Abelian varieties under the action of group endomorphisms and for lines under the action of diagonal endomorphisms of $\mathbb{P}^1 \times \mathbb{ P}^1$.
Manin–Mumford Conjecture
@inproceedings{dragos2011towards,
title={Towards a Dynamical Manin–Mumford Conjecture},
author={Dragos Ghioca, Thomas J. Tucker, and Shou-Wu Zhang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180816223542052916142},
booktitle={International Mathematics Research Notices},
volume={2011},
number={22},
pages={5109–5122},
year={2011},
}

Dragos Ghioca, Thomas J. Tucker, and Shou-Wu Zhang. Towards a Dynamical Manin–Mumford Conjecture. 2011. Vol. 2011. In International Mathematics Research Notices. pp.5109–5122. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20180816223542052916142.