The Dynamical Mordell-Lang Conjecture

Jason P. Bell, Dragos Ghioca, Thomas J. Tucker (Autoren)

Buch | Hardcover

280 Seiten

2016
American Mathematical Society (Verlag)
978-1-4704-2408-4 (ISBN)

Titel z.Zt. nicht lieferbar
Versandkostenfrei
Auch auf Rechnung

Artikel merken

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.

Jason P. Bell, University of Waterloo, Ontario, Canada. Dragos Ghioca, University of British Columbia, Vancouver, BC, Canada. Thomas J. Tucker, University of Rochester, NY, USA.

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

Erscheinungsdatum	06.05.2016
Reihe/Serie	Mathematical Surveys and Monographs
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	674 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Algebra
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
ISBN-10	1-4704-2408-8 / 1470424088
ISBN-13	978-1-4704-2408-4 / 9781470424084
Zustand	Neuware