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About: André–Oort conjecture     Goto   Sponge   NotDistinct   Permalink

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Type: yago:WikicatConjecturesyago:Abstraction100002137yago:Cognition100023271yago:Concept105835747yago:Content105809192yago:Hypothesis105888929yago:Idea105833840yago:PsychologicalFeature100023100diseaseyago:Speculation105891783 New Facet based on Instances of this Class

In mathematics, the André–Oort conjecture is a problem in Diophantine geometry, a branch of number theory, that can be seen as a non-abelian analogue of the Manin–Mumford conjecture, which is now a theorem (and is actually proven in several genuinely different ways). The conjecture concerns itself with a characterization of the Zariski closure of sets of special points in Shimura varieties.A special case of the conjecture was stated by Yves André in 1989 and a more general statement (albeit with a restriction on the type of the Shimura variety) was conjectured by Frans Oort in 1995. The modern version is a natural generalization of these two conjectures.