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Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)
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Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181)

Umberto Zannier

Abstract

This 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 the author at the Institute for Advanced Study in Princeton in May 2010.The book consists of four chapters and seven brief appendixes. The first chapter considers multiplicative algebraic groups, presenting pro ... More

Keywords: unlikely intersections, torsion points, multiplicative algebraic groups, arithmetic, Manin–Mumford issue, André–Oort conjecture, Pila

Bibliographic Information

Print publication date: 2012 Print ISBN-13: 9780691153704
Published to Princeton Scholarship Online: October 2017 DOI:10.23943/princeton/9780691153704.001.0001

Authors

Affiliations are at time of print publication.

Umberto Zannier, author
Scuola Normal Superiore