Point-counting and the Zilber-Pink conjecture

Contents
Preface
Conventions
1 Introduction
I Point-Counting and Diophantine Applications
2 Point-Counting
3 Multiplicative Manin–Mumford
4 Powers of the Modular Curve as Shimura
Varieties
5 Modular André–Oort
6 Point-Counting and the André–Oort Conjecture
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 an O-Minimal Structure
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
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