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arXiv · 0906.2559

Parametrization of abelian $K$-surfaces with quaternionic multiplication

Xavier Guitart·Santiago Molina
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Abstract

We prove that the abelian $K$-surfaces whose endomorphism algebra is a 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.

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Xavier Guitart, Santiago Molina. 2010-03-24. Parametrization of abelian $K$-surfaces with quaternionic multiplication. https://arxiv.org/abs/0906.2559

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