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André–Oort conjecture : ウィキペディア英語版
André–Oort conjecture
In mathematics, the André–Oort conjecture is an open problem in number theory that generalises the Manin–Mumford conjecture. A prototypical version of the conjecture was stated by Yves André in 1989〔.〕 and a more general version was conjectured by Frans Oort in 1995.〔.〕 The modern version is a natural generalisation of these two conjectures.
==Statement==

The conjecture in its modern form is as follows. Let ''S'' be a Shimura variety and let ''V'' be a set of special points in ''S''. Then the irreducible components of the Zariski closure of ''V'' are special subvarieties.
André's first version of the conjecture was just for one dimensional subvarieties of Shimura varieties, while Oort proposed that it should work with subvarieties of the moduli space of principally polarised Abelian varieties of dimension ''g''.

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