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The Arithmetic of Polynomial Dynamical Pairs : (AMS-214).
・ISBN 978-0-691-23547-9 paper US$ 87.00
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| 著者・編者 | Favre, Charles / Gauthier, Thomas, |
|---|---|
| シリーズ | Annals of Mathematics Studies |
| 出版社 | (Princeton University Press, US) |
| 出版年月 | 2022 |
| ページ数 | 252 pp. |
| 言語 | ENG |
| ニュース番号 | ＜M25-646＞ |
解説
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 Andre-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.