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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...
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| Main Authors: | |
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| Group Author: | |
| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, New Jersey : |
| Publication Dates: | 2022. |
| Literature type: | Book |
| Language: | English |
| Series: |
Annals of Mathematics Studies ;
volume 214 |
| Subjects: | |
| 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 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. |
| Carrier Form: | xvii, 232 pages : illustrations ; 24 cm. |
| Bibliography: | Includes bibliographical references (pages [217]-229) and index. |
| ISBN: |
9780691235462 0691235465 9780691235486 0691235481 9780691235479 0691235473 |
| Index Number: | QA161 |
| CLC: | O174.14 |
| Call Number: | O174.14/F277 |