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Let  Z = X 1  × ··· × X n   be a product of Drinfeld modular curves. We characterize those algebraic subvarieties  X ⊂ Z  containing a Zariski-dense set of CM points, i.e. points corresponding to  n -tuples of Drinfeld modules with complex multiplication (and suitable level structure). This is a characteristic  p  analogue of a special case of the André-Oort conjecture.

The André-Oort conjecture for products of Drinfeld modular curves