Towards a Dynamical Manin–Mumford Conjecture

Dragos Ghioca University of British Columbia Thomas J. Tucker University of Rochester Shou-Wu Zhang Princeton University

Algebraic Geometry Number Theory mathscidoc: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
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@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.
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