The dynamical Mordell-Lang problem for étale maps

By Jason P. Bell, Dragos Ghioca, T. Tucker. American Journal of Mathematics, 2008

101 citations recorded by the source corpus.

We prove a dynamical version of the Mordell-Lang conjecture for étale endomorphisms of quasiprojective varieties. We use $p$-adic methods inspired by the work of Skolem, Mahler, and Lech, combined with methods from algebraic geometry. As special cases of our result we obtain a new proof of the classical Mordell-Lang conjecture for cyclic subgroups of a semiabelian variety, and we also answer positively a question of Keeler/Rogalski/Stafford for critically dense sequences of closed points of a Noetherian integral scheme.

Subfields: Applied Mathematics, Geometry and Topology, Pharmacology

View Paper: https://www.semanticscholar.org/paper/07e854286482904b9c7bb21e6204d799681ead46

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

1. Joseph H. Silverman
2. Robert L. Benedetto
3. T. Tucker
4. Dragos Ghioca
5. Pär Kurlberg
6. Laura Demarco
7. Patrick Ingram
8. Shu Kawaguchi

In Geometry and Topology

1. T. Tucker
2. Joseph H. Silverman
3. Robert L. Benedetto
4. Pär Kurlberg
5. Laura Demarco
6. Dragos Ghioca
7. Shu Kawaguchi
8. Michelle Manes

In Pharmacology

1. Robert L. Benedetto
2. T. Tucker
3. Dragos Ghioca
4. Pär Kurlberg

Citations in the corpus

• Periods of rational maps modulo primes (2011, methodology): “) When this condition is met, even at a single prime of suitably good reduction, one can apply the generalized Skolem-type techniques of [5] to prove the cyclic case of the Dynamical Mordell–Lang Conjecture for and α.”
• Current trends and open problems in arithmetic dynamics (2018, background): “(b) (Bell–Ghioca–Tucker, 2010, [15]) The map f : X → X is unramified.”
• Periodic points, linearizing maps, and the dynamical Mordell–Lang problem (2008, methodology): “Furthermore, using [ BGT , Theorem 3.3] we obtain that we may take”
• Examples of dynamical degree equals arithmetic degree (2012, background): “inear recurrences and Chaubauty’s result on rational points on curves [8], as well as more recent results in arithmetic dynamics, including for example papers on the dynamical Mordell–Lang conjecture [5, 6, 10] and applications to potential density [1]. Example 21. We note that it is possible for fm”
• The Dynamical Mordell-lang Conjecture (2007, unknown): “N T ] 6 F eb 2”
• A case of the dynamical Mordell–Lang conjecture (2012, methodology): “Building on the ideas from [5], the case when " is any étale endomorphism of any quasiprojective variety was completely solved in [6].”