Abstract:
Let S 1 and S 2 be two Shimura curves over ℚ attached to rational indefinite quaternion algebras B 1 ℚ and B 1 ℚ with maximal orders B 1 and B 2 respectively. We consider an irreducible closed algebraic curve C in the product (S 1×S 2)ℂ such that C(ℂ) ∩ (S 1×S 2)(ℂ) contains infinitely many complex multiplication points. We prove, assuming the Generalized Riemann Hypothesis (GRH) for imaginary quadratic fields, that C is of Hodge type.
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Received: 3 January 2000 / Revised version: 2 October 2000
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Yafaev, A. Special points on products of two Shimura curves. manuscripta math. 104, 163–171 (2001). https://doi.org/10.1007/PL00005868
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DOI: https://doi.org/10.1007/PL00005868