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Journals and Conferences
Let Z = X1×· · ·×Xn 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.
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 derive asymptotically optimal upper bounds on the number of L-rational torsion points on a given elliptic curve or Drinfeld module defined over a finitely generated field K, as a function of the degree [L : K]. Our main tool is the adelic openness of the image of Galois representations attached to elliptic curves and Drinfeld modules, due to Serre and… (More)
Let E be a modular elliptic curve defined over a rational function field k of odd characteristic. We construct a sequence of Heegner points on E, defined over a Zp -tower of finite extensions of k, and show that these Heegner points generate a group of infinite rank. This is a function field analogue of a result of C. Cornut and V. Vatsal.
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 k be a global field, k a separable closure of k, and Gk the absolute Galois group Gal(k/k) of k over k. For every σ ∈ Gk, 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 ∈ Gk, the Mordell-Weil group E(k σ ) has infinite rank in the following two cases. Firstly when k is a global function field of… (More)
We study Ducci-sequences using basic properties of cyclotomic polynomials over F2. 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 Duccisequences, primitive polynomials and Artin’s… (More)
We study modular polynomials classifying cyclic isogenies between Drinfeld modules of arbitrary rank over the ring Fq[T ].
Cécile Armana (University of Münster) Explicit bases of modular symbols over function fields. We will discuss Teitelbaum’s theory of modular symbols over a rational function field of positive characteristic. They are an essential tool for computations of certain automorphic forms, Drinfeld modular forms and elliptic curves over such a field. As in the… (More)