Point-Counting and the Zilber-Pink Conjecture

1. Introduction; Part I. Point-Counting and Diophantine Applications: 2. Point-counting; 3. Multiplicative Manin-Mumford; 4. Powers of the Modular Curve as Shimura Varieties; 5. Modular Andre-Oort; 6. Point-Counting and the Andre-Oort Conjecture; Part II. O-Minimality and Point-Counting: 7. Model theory and definable sets; 8. O-minimal structures; 9. Parameterization and point-counting; 10. Better bounds; 11. Point-counting and Galois orbit bounds; 12. Complex analysis in O-minimal structures; Part III. Ax-Schanuel Properties: 13. Schanuel's conjecture and Ax-Schanuel; 14. A formal setting; 15. Modular Ax-Schanuel; 16. Ax-Schanuel for Shimura varieties; 17. Quasi-periods of elliptic curves; Part IV. The Zilber-Pink Conjecture: 18. Sources; 19. Formulations; 20. Some results; 21. Curves in a power of the modular curve; 22. Conditional modular Zilber-Pink; 23. O-minimal uniformity; 24. Uniform Zilber-Pink; References; List of notation; Index.

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• Teoria dos números
• Geometria algébrica
• Lógica matemática