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02504aam a2200409 i 4500 001 ACF363E438A911ED914067003BECA4DB 003 SILO 005 20220920010102 008 220707t20222022njua b 001 0 eng d 020 $a 0691235473 020 $a 9780691235479 020 $a 0691235465 020 $a 9780691235462 035 $a (OCoLC)1334669150 040 $a MZF $b eng $e rda $c MZF $d YDX $d OCLCF $d MNU $d NHM $d NUI $d SILO 050 4 $a QA161.P59 $b F38 2022 050 4 $a QA1 $b .A626 no.214 100 1 $a Favre, Charles, $e author. 245 14 $a The arithmetic of polynomial dynamical pairs / $c Charles Favre, Thomas Gauthier. 264 1 $a Princeton ; $b Princeton University Press, $c 2022. 300 $a xvii, 232 pages : $b illustrations ; $c 25 cm. 490 1 $a Annals of Mathematics Studies, $x 0066-2313 ; $v Number 214 504 $a Includes bibliographical references (pages 217-229) and index. 520 $a 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. 650 0 $a Polynomials. 650 0 $a Geometry, Algebraic. 650 0 $a Dynamics. 650 7 $a Dynamics. $2 fast $0 (OCoLC)fst00900295 650 7 $a Geometry, Algebraic. $2 fast $0 (OCoLC)fst00940902 650 7 $a Polynomials. $2 fast $0 (OCoLC)fst01070715 700 1 $a Gauthier, Thomas, $e author. 776 08 $i Online version: $a Favre, Charles. $t Arithmetic of Polynomial Dynamical Pairs. $d Princeton : Princeton University Press, 2022 $z 9780691235486 $w (OCoLC)1312165690 773 18 $w 990007568870202771 $g no:31858073074621 830 0 $a Annals of mathematics studies ; $v no. 214. 941 $a 1 952 $l OVUX522 $d 20231117013355.0 956 $a http://locator.silo.lib.ia.us/search.cgi?index_0=id&term_0=ACF363E438A911ED914067003BECA4DBInitiate Another SILO Locator Search