Some problems of unlikely intersections in arithmetic and geometry
 Responsibility
 Umberto Zannier ; with appendixes by David Masser.
 Language
 English.
 Imprint
 Princeton : Princeton University Press, 2012.
 Physical description
 xi, 160 p. ; 26 cm.
 Series
 Annals of mathematics studies ; no. 181.
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Math & Statistics Library

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QA1 .A665 NO.181

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QA1 .A665 NO.181
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Creators/Contributors
 Author/Creator
 Zannier, U. (Umberto), 1957
 Contributor
 Masser, David William, 1948
Contents/Summary
 Bibliography
 Includes bibliographical references and index.
 Publisher's Summary
 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 AndrOort conjecture (outlining work by Pila).
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Subjects
Bibliographic information
 Publication date
 2012
 Series
 Annals of mathematics studies ; no. 181
 ISBN
 9780691153704 (hardcover : acidfree paper)
 0691153701 (hardcover : acidfree paper)
 9780691153711 (pbk. : acidfree paper)
 069115371X (pbk. : acidfree paper)