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The arithmetic of polynomial dynamical pairs

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The arithmetic of polynomial dynamical pairsCharles Favre, Thomas Gauthier.
作者:	Favre, Charles.
其他作者:	Gauthier, Thomas.
出版者:	Princeton, NJ :Princeton University Press,c2022.
面頁冊數:	1 online resource (252 p.) :ill.
標題:	Polynomials.
電子資源:	https://www.degruyter.com/isbn/9780691235486
ISBN:	9780691235486$q(ebook)

The arithmetic of polynomial dynamical pairs
Favre, Charles.

The arithmetic of polynomial dynamical pairs[electronic resource] /Charles Favre, Thomas Gauthier. - Princeton, NJ :Princeton University Press,c2022. - 1 online resource (252 p.) :ill. - Annals of mathematics studies ;no. 214. - Annals of mathematics studies ;no. 37..

Includes bibliographical references and index.

New mathematical research in arithmetic dynamicsIn 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.

ISBN: 9780691235486$q(ebook)

Standard No.: 10.1515/9780691235486doiSubjects--Topical Terms:

184760
Polynomials.

LC Class. No.: QA1 / .A626

Dewey Class. No.: 512.9/422

The arithmetic of polynomial dynamical pairs
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490 1 $a Annals of mathematics studies ; $v no. 214
504 $a Includes bibliographical references and index.
520 $a New mathematical research in arithmetic dynamicsIn 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.
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650 0 $a Geometry, Algebraic. $3 190843
650 0 $a Dynamics. $3 189568
700 1 $a Gauthier, Thomas. $3 960111
830 0 $a Annals of mathematics studies ; $v no. 37. $3 697432
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