LEADER 05048nam 22009255 450 001 9910457166803321 005 20210111125649.0 010 $a1-283-45705-9 010 $a9786613457059 010 $a1-4008-4271-9 024 7 $a10.1515/9781400842711 035 $a(CKB)2550000000084277 035 $a(EBL)859035 035 $a(OCoLC)775873005 035 $a(SSID)ssj0000614574 035 $a(PQKBManifestationID)11405754 035 $a(PQKBTitleCode)TC0000614574 035 $a(PQKBWorkID)10605312 035 $a(PQKB)11066431 035 $a(DE-B1597)447247 035 $a(OCoLC)979905294 035 $a(DE-B1597)9781400842711 035 $a(MiAaPQ)EBC859035 035 $a(PPN)199244510$9sudoc 035 $a(PPN)187959641 035 $a(EXLCZ)992550000000084277 100 $a20190708d2012 fg 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt 182 $cc 183 $acr 200 10$aSome Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181) /$fUmberto Zannier 205 $aCourse Book 210 1$aPrinceton, NJ : $cPrinceton University Press, $d[2012] 210 4$d©2012 215 $a1 online resource (175 p.) 225 0 $aAnnals of Mathematics Studies ;$v205 300 $aDescription based upon print version of record. 311 $a0-691-15371-X 327 $t Frontmatter -- $tContents -- $tPreface -- $tNotation and Conventions -- $tIntroduction: An Overview of Some Problems of Unlikely Intersections -- $tChapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture -- $tChapter 2: An Arithmetical Analogue -- $tChapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser -- $tChapter 4: About the André-Oort Conjecture -- $tAppendix A: Distribution of Rational Points on Subanalytic Surfaces / $rZannier, Umberto -- $tAppendix B: Uniformity in Unlikely Intersections: An Example for Lines in Three Dimensions / $rMasser, David -- $tAppendix C: Silverman's Bounded Height Theorem for Elliptic Curves: A Direct Proof / $rMasser, David -- $tAppendix D: Lower Bounds for Degrees of Torsion Points: The Transcendence Approach / $rMasser, David -- $tAppendix E: A Transcendence Measure for a Quotient of Periods / $rMasser, David -- $tAppendix F: Counting Rational Points on Analytic Curves: A Transcendence Approach / $rMasser, David -- $tAppendix G: Mixed Problems: Another Approach / $rMasser, David -- $tBibliography -- $tIndex 330 $aThis book considers the so-called Unlikely Intersections, a topic that embraces well-known issues, such as Lang's and Manin-Mumford's, concerning torsion points in subvarieties of tori or abelian varieties. More generally, the book considers algebraic subgroups that meet a given subvariety in a set of unlikely dimension. The book is an expansion of the Hermann Weyl Lectures delivered by Umberto Zannier at the Institute for Advanced Study in Princeton in May 2010. The book consists of four chapters and seven brief appendixes, the last six by David Masser. The first chapter considers multiplicative algebraic groups, presenting proofs of several developments, ranging from the origins to recent results, and discussing many applications and relations with other contexts. The second chapter considers an analogue in arithmetic and several applications of this. The third chapter introduces a new method for approaching some of these questions, and presents a detailed application of this (by Masser and the author) to a relative case of the Manin-Mumford issue. The fourth chapter focuses on the André-Oort conjecture (outlining work by Pila). 410 0$aAnnals of Mathematics Studies 606 $aAlgebraic geometry 606 $aAlgebraic geometry 606 $aAlgebraic varieties 606 $aAlgebraic varieties 606 $aGeometry, Algebraic 606 $aIntersection theory 606 $aIntersection theory 606 $aIntersection theory (Mathematics) 606 $aAlgebraic varieties 606 $aGeometry, Algebraic 606 $aMathematics$2HILCC 606 $aPhysical Sciences & Mathematics$2HILCC 606 $aGeometry$2HILCC 608 $aElectronic books. 615 4$aAlgebraic geometry. 615 4$aAlgebraic geometry. 615 4$aAlgebraic varieties. 615 4$aAlgebraic varieties. 615 4$aGeometry, Algebraic. 615 4$aIntersection theory. 615 4$aIntersection theory. 615 0$aIntersection theory (Mathematics) 615 0$aAlgebraic varieties 615 0$aGeometry, Algebraic 615 7$aMathematics 615 7$aPhysical Sciences & Mathematics 615 7$aGeometry 676 $a516.35 686 $aSI 830$2rvk 700 $aZannier$b Umberto, $0149228 701 $aMasser$b David$049131 801 0$bDE-B1597 801 1$bDE-B1597 906 $aBOOK 912 $a9910457166803321 996 $aSome Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)$92479292 997 $aUNINA