
The Arithmetic of Polynomial Dynamical Pairs
Princeton University Press
Published on 14. June 2022
Book
Paperback/Softback
252 pages
978-0-691-23547-9 (ISBN)
Description
New mathematical research in arithmetic dynamics
In The Arithmetic of Polynomial Dynamical Pairs, 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 Andre-Oort conjecture for curves in this context, originally stated by Baker and DeMarco.
This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.
In The Arithmetic of Polynomial Dynamical Pairs, 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 Andre-Oort conjecture for curves in this context, originally stated by Baker and DeMarco.
This is a reader-friendly invitation to a new and exciting research area that brings together sophisticated tools from many branches of mathematics.
More details
Series
Language
English
Place of publication
New Jersey
United States
Target group
College/higher education
Professional and scholarly
Product notice
Paperback (trade)
Illustrations
18 b/w illus.
Dimensions
Height: 155 mm
Width: 231 mm
Thickness: 18 mm
Weight
363 gr
ISBN-13
978-0-691-23547-9 (9780691235479)
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Schweitzer Classification
Other editions
Additional editions

E-Book
06/2022
1st Edition
Princeton University Press
€81.49
Available for download
Persons
Charles Favre is a CNRS senior researcher based at the Ecole Polytechnique in Paris. He is the coauthor of The Valuative Tree and the coeditor of Berkovich Spaces and Applications. Thomas Gauthier is professor of mathematics at the Universite Paris-Saclay.