Special subvarieties of Drinfeld modular varieties

Breuer, Florian (2010-11)

Accepted for publication under copy editing

Article

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.

Please refer to this item in SUNScholar by using the following persistent URL: http://hdl.handle.net/10019.1/19870
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