The Andre-Oort conjecture for the moduli space of Abelian Surfaces

TL;DR

This paper proves the Andre-Oort conjecture unconditionally for the moduli space of principally polarized Abelian surfaces, confirming a key prediction in arithmetic geometry using a Pila-Zannier strategy.

Contribution

It provides the first unconditional proof of the Andre-Oort conjecture for $\

Findings

Unconditional proof of the Andre-Oort conjecture for $\\mathcal{A}_{2,1}$

Verification of the conjecture's predictions in the case of Abelian surfaces

Application of Pila-Zannier strategy to a new class of moduli spaces

Abstract

We provide an unconditional proof of the Andr\'e-Oort conjecture for the coarse moduli space $\mathcal{A}_{2,1}$ of principally polarized Abelian surfaces, following the strategy outlined by Pila-Zannier.