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The Dynamical Mordell-Lang Conjecture

Jason P. Bell (author) Dragos Ghioca (author)
Thomas J. Tucker (author)

ISBN: 9781470424084

Publication Date: Apr 2016

Format: Hardback

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.
£101.00

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  • Table of Contents
  • Author Biography
  • Customer Reviews
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.
Pages 280
Dimensions 254 x 178
Date Published 30 Apr 2016
Publisher American Mathematical Society
Series Mathematical Surveys and Monographs
Series Part 210
Subject/s Algebra   Number theory   Algebraic geometry  
  • 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
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.

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