The Dynamical Mordell–Lang Conjecture
- ISBN-10
- 1470424088
- ISBN-13
- 9781470424084
- Category
- Arithmetical algebraic geometry
- Pages
- 280
- Language
- English
- Published
- 2016-04-20
- Publisher
- American Mathematical Soc.
- Authors
- Jason P. Bell, Dragos Ghioca, Thomas J. Tucker
Description
The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of the orbit of a point x under the action of an endomorphism f of a quasiprojective complex variety X. More precisely, it claims that for any point x in X and any subvariety V of X, the set of indices n such that the n-th iterate of x under f lies in V is a finite union of arithmetic progressions. In this book the authors present all known results about the Dynamical Mordell-Lang Conjecture, focusing mainly on a p-adic approach which provides a parametrization of the orbit of a point under an endomorphism of a variety.
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