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Let X be a product of Drinfeld modular curves over a general base ring A of odd characteristic. We classify those subvarieties of X which contain a Zariski-dense subset of CM points. This is an analogue of the André-Oort conjecture. As an application, we construct non-trivial families of higher Heegner points on modular elliptic curves over global function(More)
Let ϕ be a non-isotrivial family of Drinfeld A-modules of rank r in generic characteristic with a suitable level structure over a connected smooth algebraic variety X. Suppose that the endomorphism ring of ϕ is equal to A. Then we show that the closure of the analytic fundamental group of X in SLr(A f F) is open, where A f F denotes the ring of finite(More)
We study Ducci-sequences using basic properties of cyclotomic polynomials over F 2. We determine the period of a given Ducci-sequence in terms of the order of a polynomial, and in terms of the multiplicative orders of certain elements in finite fields. We also compute some examples and study links between Ducci-sequences, primitive polynomials and Artin's(More)
Let k be a global field, k a separable closure of k, and G k the absolute Galois group Gal(k/k) of k over k. For every σ ∈ G k , let k σ be the fixed subfield of k under σ. Let E/k be an elliptic curve over k. We show that for each σ ∈ G k , the Mordell-Weil group E(k σ) has infinite rank in the following two cases. Firstly when k is a global function field(More)
We explore an analogue of the André-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(More)
Let K be a number field and E/K a modular elliptic curve, with modular parametriza-tion π : X 0 (N) −→ E defined over K. The purpose of this note is to study the images in E of classes of isogenous points in X 0 (N). Theorem 1 Let S ⊂ X 0 (N)(¯ K) be an infinite set of points corresponding to elliptic curves which all lie in one isogeny class, but which are(More)