The Andr\'e-Oort conjecture via o-minimality

TL;DR

This paper explains the Pila-Zannier strategy for proving the André-Oort conjecture, providing an introduction to Shimura varieties and their role in the proof.

Contribution

It clarifies the Pila-Zannier approach and offers foundational insights into Shimura varieties relevant to the conjecture.

Findings

Outline of the Pila-Zannier strategy

Introduction to Shimura varieties

Connection to André-Oort conjecture

Abstract

The purpose of this article is to explain the Pila-Zannier strategy for proving the Andr\'e-Oort conjecture. First, however, we will provide a brief introduction to the theory of Shimura varieties.