Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture

Kapitel in diesem Buch

1. Frontmatter i
2. Contents v
3. Preface ix
4. Notation and Conventions xi
5. Introduction: An Overview of Some Problems of Unlikely Intersections 1
6. Chapter 1: Unlikely Intersections in Multiplicative Groups and the Zilber Conjecture 15
7. Chapter 2: An Arithmetical Analogue 43
8. Chapter 3 Unlikely Intersections in Elliptic Surfaces and Problems of Masser 62
9. Chapter 4: About the André-Oort Conjecture 96
10. Appendix A: Distribution of Rational Points on Subanalytic Surfaces 128
11. Appendix B: Uniformity in Unlikely Intersections: An Example for Lines in Three Dimensions 136
12. Appendix C: Silverman's Bounded Height Theorem for Elliptic Curves: A Direct Proof 138
13. Appendix D: Lower Bounds for Degrees of Torsion Points: The Transcendence Approach 140
14. Appendix E: A Transcendence Measure for a Quotient of Periods 143
15. Appendix F: Counting Rational Points on Analytic Curves: A Transcendence Approach 145
16. Appendix G: Mixed Problems: Another Approach 147
17. Bibliography 149
18. Index 159