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

By Jonathan Pila, Jacob Tsimerman. Compositio Mathematica, 2011

69 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9c84b4a9ec841e013e3ef14c3ed20eb7fdad8362

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In Geometry and Topology

1. Ziyang Gao
2. Jacob Tsimerman
3. Jonathan Pila
4. Bruno Klingler
5. P. Habegger
6. E. Ullmo
7. Fabrizio Barroero
8. Martin Widmer

In Mathematical Physics

1. Ziyang Gao
2. Jacob Tsimerman
3. Jonathan Pila
4. Bruno Klingler
5. E. Ullmo
6. Benjamin Bakker
7. Manjul Bhargava

Citations in the corpus

• Ax-Schanuel for Shimura varieties (2017, unknown): “The proof follows the corresponding deduction in [30].”
• Ax-Lindemann for $\mathcal{A}_g$ (2014, methodology): “Then by Theorem 3.1 in [28] we know that H ( Z ) ≺ | Disc( R x ) | , where H ( Z ) is the height of the point Z .”
• Towards the Andr\'e-Oort conjecture for mixed Shimura varieties: the Ax-Lindemann theorem and lower bounds for Galois orbits of special points (2013, background): “product of universal families of elliptic curves [48](1)), Ullmo-Yafaev (for projective pure Shimura varieties [64]) and Pila-Tsimerman (for A2 [50] and then Ag [49]).”