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Moduli Spaces and Arithmetic Dynamics
 
Joseph H. Silverman Brown University, Providence, RI
A co-publication of the AMS and Centre de Recherches Mathématiques
Moduli Spaces and Arithmetic Dynamics
Hardcover ISBN:  978-0-8218-7582-7
Product Code:  CRMM/30
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-0-8218-8502-4
Product Code:  CRMM/30.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-7582-7
eBook: ISBN:  978-0-8218-8502-4
Product Code:  CRMM/30.B
List Price: $225.00 $170.00
MAA Member Price: $202.50 $153.00
AMS Member Price: $180.00 $136.00
Moduli Spaces and Arithmetic Dynamics
Click above image for expanded view
Moduli Spaces and Arithmetic Dynamics
Joseph H. Silverman Brown University, Providence, RI
A co-publication of the AMS and Centre de Recherches Mathématiques
Hardcover ISBN:  978-0-8218-7582-7
Product Code:  CRMM/30
List Price: $115.00
MAA Member Price: $103.50
AMS Member Price: $92.00
eBook ISBN:  978-0-8218-8502-4
Product Code:  CRMM/30.E
List Price: $110.00
MAA Member Price: $99.00
AMS Member Price: $88.00
Hardcover ISBN:  978-0-8218-7582-7
eBook ISBN:  978-0-8218-8502-4
Product Code:  CRMM/30.B
List Price: $225.00 $170.00
MAA Member Price: $202.50 $153.00
AMS Member Price: $180.00 $136.00
  • Book Details
     
     
    CRM Monograph Series
    Volume: 302012; 140 pp
    MSC: Primary 37; Secondary 14;

    This monograph studies moduli problems associated to algebraic dynamical systems. It is an expanded version of the notes for a series of lectures delivered at a workshop on Moduli Spaces and the Arithmetic of Dynamical Systems at the Bellairs Research Institute, Barbados, in 2010.

    The author's goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this exciting area of current research. Topics covered include:

    (1) Construction and properties of dynamical moduli spaces for self-maps of projective space.

    (2) Dynatomic modular curves for the space of quadratic polynomials.

    (3) The theory of canonical heights associated to dynamical systems.

    (4) Special loci in dynamical moduli spaces, in particular the locus of post-critically finite maps.

    (5) Field of moduli and fields of definition for dynamical systems.

    Titles in this series are co-published with the Centre de recherches mathématiques.

    Readership

    Graduate students and research mathematicians interested in dynamical systems, number theory, and algebraic geometry.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • Moduli spaces associated to dynamical systems
    • The geometry of dynamical moduli spaces
    • Dynamical moduli spaces–Further topics
    • Dynatomic polynomials and dynamical modular curves
    • Canonical heights
    • Postcritically finite maps
    • Field of moduli and field of definition
  • Reviews
     
     
    • The monograph is an expanded version of Silverman's lecture notes from a workshop held in May 2010, on the topic of moduli spaces of dynamical systems. It is a pleasure to read, as much as it was a pleasure to attend the lectures. Silverman writes well: he explains the mathematics clearly and includes many explicit examples. Best of all, he has peppered the text with leading questions and side remarks, opening doors to hundreds of potential research projects. It will be a useful reference for students and senior researchers alike. ...Every chapter of this monograph offers multiple entries, many conjectural, in the "Silverman dictionary." For anyone already familiar with both the arithmetic theory of elliptic curves and the traditionally analytic results about these dynamical systems, recent results in arithmetic dynamics make the analogies beautifully apparent; with this book, Silverman helps the rest of us to appreciate the similarities.

      Laura De Marco, University of Illinois at Chicago
  • Requests
     
     
    Review Copy – for publishers of book reviews
    Accessibility – to request an alternate format of an AMS title
Volume: 302012; 140 pp
MSC: Primary 37; Secondary 14;

This monograph studies moduli problems associated to algebraic dynamical systems. It is an expanded version of the notes for a series of lectures delivered at a workshop on Moduli Spaces and the Arithmetic of Dynamical Systems at the Bellairs Research Institute, Barbados, in 2010.

The author's goal is to provide an overview, with enough details and pointers to the existing literature, to give the reader an entry into this exciting area of current research. Topics covered include:

(1) Construction and properties of dynamical moduli spaces for self-maps of projective space.

(2) Dynatomic modular curves for the space of quadratic polynomials.

(3) The theory of canonical heights associated to dynamical systems.

(4) Special loci in dynamical moduli spaces, in particular the locus of post-critically finite maps.

(5) Field of moduli and fields of definition for dynamical systems.

Titles in this series are co-published with the Centre de recherches mathématiques.

Readership

Graduate students and research mathematicians interested in dynamical systems, number theory, and algebraic geometry.

  • Chapters
  • Introduction
  • Moduli spaces associated to dynamical systems
  • The geometry of dynamical moduli spaces
  • Dynamical moduli spaces–Further topics
  • Dynatomic polynomials and dynamical modular curves
  • Canonical heights
  • Postcritically finite maps
  • Field of moduli and field of definition
  • The monograph is an expanded version of Silverman's lecture notes from a workshop held in May 2010, on the topic of moduli spaces of dynamical systems. It is a pleasure to read, as much as it was a pleasure to attend the lectures. Silverman writes well: he explains the mathematics clearly and includes many explicit examples. Best of all, he has peppered the text with leading questions and side remarks, opening doors to hundreds of potential research projects. It will be a useful reference for students and senior researchers alike. ...Every chapter of this monograph offers multiple entries, many conjectural, in the "Silverman dictionary." For anyone already familiar with both the arithmetic theory of elliptic curves and the traditionally analytic results about these dynamical systems, recent results in arithmetic dynamics make the analogies beautifully apparent; with this book, Silverman helps the rest of us to appreciate the similarities.

    Laura De Marco, University of Illinois at Chicago
Review Copy – for publishers of book reviews
Accessibility – to request an alternate format of an AMS title
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