Parametrization of Abelian K-surfaces with quaternionic multiplication
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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.
CitationGuitart, X.; Molina, S. Parametrization of Abelian K-surfaces with quaternionic multiplication. "Comptes Rendus de l'Académie des Sciences. Series I, Mathematics", Desembre 2009, vol. 347, núm. 23-24, p. 1325-1330.