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The dynamical Mordell-Lang problem for étale maps
- American Journal of Mathematics
- Johns Hopkins University Press
- Volume 132, Number 6, December 2010
- pp. 1655-1675
- 10.1353/ajm.2010.a404144
- Article
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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.