The arithmetic of polynomial dynamical pairs / Charles Favre, Thomas Gauthier.

Format:

Book

Author/Creator:

Favre, Charles, author.

Gauthier, Thomas, author.

Series:

Annals of mathematics studies ; number 214.

Princeton scholarship online.

Annals of mathematics studies ; number 214

Princeton scholarship online

Language:

English

Subjects (All):

Polynomials.

Geometry, Algebraic.

Dynamics.

Physical Description:

1 online resource (253 p.)

Place of Publication:

Princeton : Princeton University Press, [2023]

Summary:

Charles Favre and Thomas Gauthier present new mathematical research in the field of arithmetic dynamics. Specifically, the authors study one-dimensional algebraic families of pairs given by a polynomial with a marked point. Combining tools from arithmetic geometry and holomorphic dynamics, they prove an 'unlikely intersection' statement for such pairs, thereby demonstrating strong rigidity features for them. They further describe one-dimensional families in the moduli space of polynomials containing infinitely many postcritically finite parameters, proving the dynamical André-Oort conjecture for curves in this context, originally stated by Baker and DeMarco.

Contents:

Frontmatter

Contents

List of figures

Preface

List of abbreviations

Introduction

Chapter One. Geometric background

Chapter Two. Polynomial dynamics

Chapter Three. Dynamical symmetries

Chapter Four. Polynomial dynamical pairs

Chapter Five. Entanglement of dynamical pairs

Chapter Six. Entanglement of marked points

Chapter Seven. The unicritical family

Chapter Eight. Special curves in the parameter space of polynomials

Notes

Bibliography

Index

Notes:

Previously issued in print: 2022.

Description based on online resource; title from PDF title page (viewed on June 8, 2023).

Includes bibliographical references and index.

ISBN:

9780691235486

0691235481

OCLC:

1312165690