Special Points on Products of Modular Curves
نویسنده
چکیده
We prove the André–Oort conjecture on special points of Shimura varieties for arbitrary products of modular curves, assuming the Generalized Riemann Hypothesis. More explicitly, this means the following. Let n ≥ 0, and let Σ be a subset of Cn consisting of points all of whose coordinates are j-invariants of elliptic curves with complex multiplications. Then we prove (under GRH) that the irreducible components of the Zariski closure of Σ are special subvarieties, i.e., determined by isogeny conditions on coordinates and pairs of coordinates. A weaker variant is proved unconditionally. AMS classification: 14G35, 14K22, 11G15.
منابع مشابه
The André-Oort conjecture for products of Drinfeld modular curves
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