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Some Problems of Unlikely Intersections in Arithmetic and Geometry (Am181) (Annals of Mathematics Studies)by U. Zannier
Synopses & ReviewsPublisher Comments:This book considers the socalled Unlikely Intersections, a topic that embraces wellknown issues, such as Lang's and ManinMumford'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 ManinMumford issue. The fourth chapter focuses on the AndréOort conjecture (outlining work by Pila). Synopsis:This book considers the socalled Unlikely Intersections, a topic that embraces wellknown issues, such as Lang's and ManinMumford'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 ManinMumford issue. The fourth chapter focuses on the AndréOort conjecture (outlining work by Pila). Synopsis:This book considers the socalled Unlikely Intersections, a topic that embraces wellknown issues, such as Lang's and ManinMumford'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 ManinMumford issue. The fourth chapter focuses on the AndréOort conjecture (outlining work by Pila). About the AuthorUmberto Zannier is professor of mathematics at the Scuola Normale Superiore di Pisa in Pisa, Italy. He is the author of "Lecture Notes on Diophantine Analysis" and the editor of "Diophantine Geometry."
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Related SubjectsScience and Mathematics » Mathematics » Basics Science and Mathematics » Mathematics » Geometry » Algebraic Geometry Science and Mathematics » Mathematics » Geometry » Geometry and Trigonometry Science and Mathematics » Mathematics » Group Theory 

