# The André–Oort conjecture for the moduli space of abelian surfaces

@article{Pila2012TheAC, title={The Andr{\'e}–Oort conjecture for the moduli space of abelian surfaces}, author={Jonathan Pila and Jacob Tsimerman}, journal={Compositio Mathematica}, year={2012}, volume={149}, pages={204 - 216} }

Abstract We provide an unconditional proof of the André–Oort conjecture for the coarse moduli space 𝒜2,1 of principally polarized abelian surfaces, following the strategy outlined by Pila–Zannier.

## 55 Citations

The André-Oort conjecture for A g

- Mathematics
- 2017

We give a proof of the André-Oort conjecture for Ag — the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven “averaged” version of the Colmez…

A proof of the Andre-Oort conjecture for A_g

- Mathematics
- 2015

We give a proof of the Andre-Oort conjecture for $\mathcal{A}_g$ - the moduli space of principally polarized abelian varieties. In particular, we show that a recently proven `averaged' version of the…

The André-Oort conjecture via o-minimality

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- 2014

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.

Holomorphic curves in Shimura varieties

- MathematicsArchiv der Mathematik
- 2018

We prove a hyperbolic analogue of the Bloch–Ochiai theorem about the Zariski closure of holomorphic curves in abelian varieties. We consider the case of non compact Shimura varieties completing the…

Canonical Heights on Shimura Varieties and the Andr\'e-Oort Conjecture

- Mathematics
- 2021

The main purpose of this work is to prove the Andr\'e-Oort conjecture in full generality.

SPECIAL POINT PROBLEMS WITH ELLIPTIC MODULAR SURFACES

- Mathematics
- 2014

We prove a “special point” result for products of elliptic modular surfaces, elliptic curves, multiplicative groups and complex lines, and deduce a result about vanishing linear combinations of…

Hyperbolic Ax–Lindemann theorem in the cocompact case

- Mathematics
- 2014

We prove an analogue of the classical Ax-Lindemann theorem in the context of compact Shimura varieties. Our work is motivated by J. Pila's strategy for proving the Andr\'e-Oort conjecture…

The hyperbolic Ax-Lindemann-Weierstraß conjecture

- Mathematics
- 2013

The hyperbolic Ax-Lindemann-Weierstrass conjecture is a functional algebraic independence statement for the uniformizing map of an arithmetic variety. In this paper we provide a proof of this…

Finiteness theorems for K3 surfaces and abelian varieties of CM type

- MathematicsCompositio Mathematica
- 2018

We study abelian varieties and K3 surfaces with complex multiplication defined over number fields of fixed degree. We show that these varieties fall into finitely many isomorphism classes over an…

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