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Some Problems of Unlikely Intersections in Arithmetic and Geometry [electronic resource].

By: Zannier, Umberto.
Contributor(s): Masser, David.
Material type: materialTypeLabelBookSeries: Annals of mathematics studies: no. 181.Publisher: Princeton : Princeton University Press, 2012Description: 1 online resource (175 pages).Content type: text Media type: computer Carrier type: online resourceISBN: 9781400842711; 1400842719; 9780691153704; 0691153701; 9780691153711; 069115371X.Subject(s): Intersection theory | Algebraic varieties | Geometry, Algebraic | Algebraic geometry | Intersection theory | Algebraic varieties | Geometry, Algebraic | MATHEMATICS -- Geometry -- Algebraic | Algebraic varieties | Geometry, Algebraic | Intersection theoryGenre/Form: Electronic books.Additional physical formats: Print version:: No titleDDC classification: 516.3/5 | 516.35 Online resources: Click here to access online
Contents:
Cover; Title; Copyright; Contents; Preface; Notation and Conventions; Introduction: An Overview of Some Problems of Unlikely Intersections; 1 Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture; 1.1 Torsion points on subvarieties of G; 1.2 Higher multiplicative rank; 1.3 Remarks on Theorem 1.3 and its developments; 1.3.1 Fields other than Q; 1.3.2 Weakened assumptions; 1.3.3 Unlikely intersections of positive dimension and height bounds; 1.3.4 Unlikely intersections of positive dimension and Zilber's conjecture.
Summary: 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 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 multipli.
List(s) this item appears in: New Arrivals Dec 2019
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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 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 multipli.

Cover; Title; Copyright; Contents; Preface; Notation and Conventions; Introduction: An Overview of Some Problems of Unlikely Intersections; 1 Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture; 1.1 Torsion points on subvarieties of G; 1.2 Higher multiplicative rank; 1.3 Remarks on Theorem 1.3 and its developments; 1.3.1 Fields other than Q; 1.3.2 Weakened assumptions; 1.3.3 Unlikely intersections of positive dimension and height bounds; 1.3.4 Unlikely intersections of positive dimension and Zilber's conjecture.

Includes bibliographical references and index.

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