Volume: 30; 2012; 140 pp; Hardcover
MSC: Primary 37; Secondary 14
Print ISBN: 978-0-8218-7582-7
Product Code: CRMM/30
List Price: $63.00
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MAA Member Price: $56.70
Electronic ISBN: 978-0-8218-8502-4
Product Code: CRMM/30.E
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Moduli Spaces and Arithmetic Dynamics
Share this pageJoseph H. Silverman
A co-publication of the AMS and Centre de Recherches Mathématiques
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.
Reviews & Endorsements
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
Table of Contents
Table of Contents
Moduli Spaces and Arithmetic Dynamics
- Cover Cover11
- Title page iii4
- Contents v6
- Preface vii8
- Introduction 110
- Moduli spaces associated to dynamical systems 312
- The geometry of dynamical moduli spaces 1120
- Dynamical moduli spaces–Further topics 4554
- Dynatomic polynomials and dynamical modular curves 5766
- Canonical heights 6978
- Postcritically finite maps 91100
- Field of moduli and field of definition 113122
- Schedule of talks at the Bellairs workshop 121130
- Glossary 123132
- Bibliography 127136
- Index 133142
- Back Cover Back Cover1151