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The Dynamical Mordell–Lang Conjecture
 
Jason P. Bell University of Waterloo, Waterloo, Ontario, Canada
Dragos Ghioca University of British Columbia, Vancouver, BC, Canada
Thomas J. Tucker University of Rochester, Rochester, NY
Front Cover for The Dynamical Mordell--Lang Conjecture
Available Formats:
Hardcover ISBN: 978-1-4704-2408-4
Product Code: SURV/210
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Electronic ISBN: 978-1-4704-2908-9
Product Code: SURV/210.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
Front Cover for The Dynamical Mordell--Lang Conjecture
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  • Front Cover for The Dynamical Mordell--Lang Conjecture
  • Back Cover for The Dynamical Mordell--Lang Conjecture
The Dynamical Mordell–Lang Conjecture
Jason P. Bell University of Waterloo, Waterloo, Ontario, Canada
Dragos Ghioca University of British Columbia, Vancouver, BC, Canada
Thomas J. Tucker University of Rochester, Rochester, NY
Available Formats:
Hardcover ISBN:  978-1-4704-2408-4
Product Code:  SURV/210
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Electronic ISBN:  978-1-4704-2908-9
Product Code:  SURV/210.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Bundle Print and Electronic Formats and Save!
This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.
List Price: $165.00
MAA Member Price: $148.50
AMS Member Price: $132.00
  • Book Details
     
     
    Mathematical Surveys and Monographs
    Volume: 2102016; 280 pp
    MSC: Primary 11; 14; 37;

    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.

    Readership

    Graduate students and research mathematicians interested in algebraic geometry and its arithmetic applications.

  • Table of Contents
     
     
    • Chapters
    • Chapter 1. Introduction
    • Chapter 2. Background material
    • Chapter 3. The dynamical Mordell-Lang problem
    • Chapter 4. A geometric Skolem-Mahler-Lech theorem
    • Chapter 5. Linear relations between points in polynomial orbits
    • Chapter 6. Parametrization of orbits
    • Chapter 7. The split case in the dynamical Mordell-Lang conjecture
    • Chapter 8. Heuristics for avoiding ramification
    • Chapter 9. Higher dimensional results
    • Chapter 10. Additional results towards the dynamical Mordell-Lang conjecture
    • Chapter 11. Sparse sets in the dynamical Mordell-Lang conjecture
    • Chapter 12. Denis-Mordell-Lang conjecture
    • Chapter 13. Dynamical Mordell-Lang conjecture in positive characteristic
    • Chapter 14. Related problems in arithmetic dynamics
    • Chapter 15. Future directions
  • Reviews
     
     
    • ...[S]uitable for experts working on problems related to the dynamical Mordell-Lang conjecture. It may also be of interest to anyone who is interested in dynamics or number theory.

      Liang-Chung Hsia, Mathematical Reviews
  • Requests
     
     
    Review Copy – for reviewers who would like to review an AMS book
    Permission – for use of book, eBook, or Journal content
    Accessibility – to request an alternate format of an AMS title
Volume: 2102016; 280 pp
MSC: Primary 11; 14; 37;

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.

Readership

Graduate students and research mathematicians interested in algebraic geometry and its arithmetic applications.

  • Chapters
  • Chapter 1. Introduction
  • Chapter 2. Background material
  • Chapter 3. The dynamical Mordell-Lang problem
  • Chapter 4. A geometric Skolem-Mahler-Lech theorem
  • Chapter 5. Linear relations between points in polynomial orbits
  • Chapter 6. Parametrization of orbits
  • Chapter 7. The split case in the dynamical Mordell-Lang conjecture
  • Chapter 8. Heuristics for avoiding ramification
  • Chapter 9. Higher dimensional results
  • Chapter 10. Additional results towards the dynamical Mordell-Lang conjecture
  • Chapter 11. Sparse sets in the dynamical Mordell-Lang conjecture
  • Chapter 12. Denis-Mordell-Lang conjecture
  • Chapter 13. Dynamical Mordell-Lang conjecture in positive characteristic
  • Chapter 14. Related problems in arithmetic dynamics
  • Chapter 15. Future directions
  • ...[S]uitable for experts working on problems related to the dynamical Mordell-Lang conjecture. It may also be of interest to anyone who is interested in dynamics or number theory.

    Liang-Chung Hsia, Mathematical Reviews
Review Copy – for reviewers who would like to review an AMS book
Permission – for use of book, eBook, or Journal content
Accessibility – to request an alternate format of an AMS title
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