The Arithmetic of Polynomial Dynamical Pairs: (Ams-214) (Paperback) (ISBN-13: 9780691235479)

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 André-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.

Author: Charles Favre, Thomas Gauthier
ISBN-10: 0691235473
ISBN-13: 9780691235479
Publisher: Princeton University Press
Language: English
Published: 06/14/2022
Pages: 252
Format: Paperback
Weight: 0.80lbs
Size: 6.10h x 9.10w x 0.70d