Special subvarieties of Drinfeld modular varieties
Accepted for publication under copy editing
We explore an analogue of the Andr´e-Oort conjecture for subvarieties of Drinfeld modular varieties. The conjecture states that a subvariety X of a Drinfeld modular variety contains a Zariski-dense set of complex multiplication (CM) points if and only if X is a “special” subvariety (i.e. X is defined by requiring additional endomorphisms). We prove this conjecture in two cases. Firstly when X contains a Zariski-dense set of CM points which all lie in one Hecke orbit, and secondly when X is a curve containing infinitely many CM points without any additional assumptions.