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The Dynamical Mordell-Lang Conjecture (Mathematical Surveys and Monographs

The Dynamical Mordell-Lang Conjecture (Mathematical Surveys and Monographs

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  • Release Date: 30/04/2016
  • Barcode: 9781470424084
  • Genre: Science Nature & Math
  • Imprint Family: American Mathematical Society
  • Label: American Mathematical Society
  • Publisher Family: American Mathematical Society
  • Publisher: American Mathematical Society
The Dynamical Mordell-Lang Conjecture (Mathematical Surveys and Monographs

The Dynamical Mordell-Lang Conjecture (Mathematical Surveys and Monographs

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DESCRIPTION

The Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. This volume presents all known results of 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.
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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