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The André-Oort conjecture via o-minimality
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O-Minimality and Diophantine Geometry
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1 the case of Abelian varieties (respectively algebraic tori), where special subvarieties are the translates of Abelian subvarieties (respectively subtori) by torsion points. A key property of special subvarieties is that connected components of their intersections are themselves special subvarieties. Thus, any subvariety Y of S is contained in a smallest special subvariety. If this happens to be a connected component of S itself, then we say that Y is Hodge generic in S. We refer to the

doi:10.1017/cbo9781316106839.006
fatcat:fbdwpw2lnrdajazgrnwd7f3pwa