Abstract
We prove that the Abelian K-surfaces whose endomorphism algebra is a rational quaternion algebra are parametrized, up to isogeny, by the K-rational points of the quotient of certain Shimura curves by the group of their Atkin–Lehner involutions. To cite this article: X. Guitart, S. Molina, C. R. Acad. Sci. Paris, Ser. I 347 (2009).
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