André-Oort conjecture for arithmetic varieties

Let Γ\X+\Gamma\backslash X^+ be an arithmetic variety, let VV be an algebraic subvariety, and let Σ\Sigma be the set of special points of Γ\X+\Gamma\backslash X^+ that belong to VV. André-Oort conjecture. The Zariski closure of Σ\Sigma is a finite union of special subvarieties of Γ\X+\Gamma\backslash X^+. The source states that this conjecture has been proved, so it is included as a resolved conjecture rather than an open problem.

Sources & referencesView supporting material

Primary source

Rodolphe Richard and Andrei Yafaev, “A Common Generalisation of the André-Oort and André-Pink-Zannier Conjectures”, arXiv:2401.03528 (2024).

Additional references

20 papers in this index state this conjecture (1999–2024). The statement above is taken from the most recent of them; the others are arXiv:2306.02290, arXiv:2112.13814, arXiv:2103.15717, arXiv:1812.04341, arXiv:1711.09387, arXiv:1607.07843, arXiv:1506.01466, arXiv:1503.07332, arXiv:1502.00822, arXiv:1405.6053, arXiv:1209.0934, arXiv:1209.0939, and 7 more.

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