The André-Oort conjecture

By Bruno Klingler, A. Yafaev. 2012

97 citations recorded by the source corpus.

In this paper we prove, assuming the Generalized Riemann Hypothesis, the Andre-Oort conjecture on the Zariski closure of sets of special points in a Shimura variety. In the case of sets of special points satisfying an additional assumption, we prove the conjecture without assuming the GRH

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/222bdaf9645e1f8f4e1175cd66326a4e97ee216b

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In Algebra and Number Theory

1. Jacob Tsimerman
2. E. Ullmo
3. Jonathan Pila
4. Jinbo Ren
5. Christopher Daw
6. Frans Oort
7. B. Moonen
8. A. Yafaev

In Geometry and Topology

1. Jacob Tsimerman
2. Jonathan Pila
3. E. Ullmo
4. B. Moonen
5. A. Yafaev
6. Ziyang Gao
7. Jinbo Ren
8. Christopher Daw

In Mathematical Physics

1. Jonathan Pila
2. Jacob Tsimerman
3. E. Ullmo
4. A. Yafaev
5. Jinbo Ren
6. Christopher Daw
7. Frans Oort
8. Ziyang Gao

Citations in the corpus

• Galois orbits and equidistribution of special subvarieties: towards the André-Oort conjecture (2012, methodology): “The part (i) of the previous lemma will not be used in this text but will play a role in [11].”
• Ax-Lindemann for $\mathcal{A}_g$ (2014, methodology): “A full proof of AO under the assumption of GRH for CM fields has been announced by Klingler, Ullmo, and Yafaev [18], [42].”
• The Torelli locus and special subvarieties (2011, methodology): “See for instance [46], Theorem 5.7, later refined by Yafaev in [82], Theorem 1.2 of [28], and Theorem 1.2.1 (with condition (2)) of [37].”
• Applications of the hyperbolic Ax–Schanuel conjecture (2017, background): “ponent XH of XH contained in X such that Z is the image of XH in Γ\X. In fact, these choices are well-defined up to conjugation by Γ. By the degree deg(Z) of Z, we refer to the degree (in the sense of [23], Section 5.1) of the Zariski closure of Z in the Baily-Borel compactification of S with respect ”