André-Oort conjecture for arithmetic varieties
André-Oort conjecture for arithmetic varieties
Let be an arithmetic variety, let be an algebraic subvariety, and let be the set of special points of that belong to . André-Oort conjecture. The Zariski closure of is a finite union of special subvarieties of . 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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