The Arithmetic of Polynomial Dynamical Pairs / Charles Favre, Thomas Gauthier.
By: Favre, Charles
.
Contributor(s): Gauthier, Thomas.
Material type: 
BookSeries: Annals of mathematics studies: Publisher: Princeton : Princeton University Press, 2022Description: 1 online resource (253 p.).Content type: text | still image Media type: unmediated Carrier type: volumeISBN: 9780691235486; 0691235481; 0691235465; 9780691235462; 0691235473; 9780691235479.Subject(s): Polynomials | Geometry, Algebraic | Dynamics | Dynamics | Geometry, Algebraic | Polynomials | MATHEMATICS / Geometry / AlgebraicGenre/Form: Electronic books.Additional physical formats: Print version:: The Arithmetic of Polynomial Dynamical PairsDDC classification: 512.9/422 Online resources: Click here to access online Summary: 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�e-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.
Description based upon print version of record.
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�e-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.
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