The Arithmetic of Polynomial Dynamical Pairs: (Ams-214) (Annals of Mathematics Studies #400) (Hardcover)

The Arithmetic of Polynomial Dynamical Pairs: (Ams-214) (Annals of Mathematics Studies #400) By Charles Favre, Thomas Gauthier Cover Image

The Arithmetic of Polynomial Dynamical Pairs: (Ams-214) (Annals of Mathematics Studies #400) (Hardcover)

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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 Andr -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.

Product Details ISBN: 9780691235462
ISBN-10: 0691235465
Publisher: Princeton University Press
Publication Date: June 14th, 2022
Pages: 252
Language: English
Series: Annals of Mathematics Studies