Opis: The Dynamical Mordell-Lang Conjecture - Dragos Ghioca, Jason Bell

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.* Introduction* Background material* The dynamical Mordell-Lang problem* A geometric Skolem-Mahler-Lech theorem* Linear relations between points in polynomial orbits* Parametrization of orbits* The split case in the dynamical Mordell-Lang conjecture* Heuristics for avoiding ramification* Higher dimensional results* Additional results towards the dynamical Mordell-Lang conjecture* Sparse sets in the dynamical Mordell-Lang conjecture* Denis-Mordell-Lang conjecture* Dynamical Mordell-Lang conjecture in positive characteristic* Related problems in arithmetic dynamics* Future directions* Bibliography* Index

Szczegóły: The Dynamical Mordell-Lang Conjecture - Dragos Ghioca, Jason Bell

Tytuł: The Dynamical Mordell-Lang Conjecture
Autor: Dragos Ghioca, Jason Bell
Wydawnictwo: American Mathematical Society
ISBN: 9781470424084
Rok wydania: 2016
Ilość stron: 280
Oprawa: Twarda

Recenzje: The Dynamical Mordell-Lang Conjecture - Dragos Ghioca, Jason Bell