Some Problems of Unlikely Intersections in Arithmetic and Geometry (AM-181) / / Umberto Zannier.

• Superior document: Title is part of eBook package: De Gruyter Princeton Annals of Mathematics eBook-Package 1940-2020
• VerfasserIn: Zannier, Umberto,
• MitwirkendeR: Masser, David,; Zannier, Umberto,
• TeilnehmendeR: Masser, David.
• Place / Publishing House: Princeton, NJ : : Princeton University Press, , [2012]; ©2012
• Year of Publication: 2012
• Edition: Course Book
• Language: English
• Series: Annals of Mathematics Studies ; 181
• Physical Description: 1 online resource (176 p.)

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...

Table of Contents

• Frontmatter
• Contents
• Preface
• Notation and Conventions
• Introduction: An Overview of Some Problems of Unlikely Intersections
• Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture
• Chapter 2: An Arithmetical Analogue
• Chapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser
• Chapter 4: About the André-Oort Conjecture
• Appendix A: Distribution of Rational Points on Subanalytic Surfaces
• Appendix B: Uniformity in Unlikely Intersections: An Example for Lines in Three Dimensions
• Appendix C: Silverman's Bounded Height Theorem for Elliptic Curves: A Direct Proof
• Appendix D: Lower Bounds for Degrees of Torsion Points: The Transcendence Approach
• Appendix E: A Transcendence Measure for a Quotient of Periods
• Appendix F: Counting Rational Points on Analytic Curves: A Transcendence Approach
• Appendix G: Mixed Problems: Another Approach
• Bibliography
• Index