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