Parametrization of abelian $K$-surfaces with quaternionic multiplication

Details Parametrization of abelian $K$-surfaces with quaternionic multiplication Parametrization of abelian $K$-surfaces with quaternionic multiplication

2009-06-14

arxiv.org/abs/0906.2559v2

C. R. Math. Acad. Sci. Paris 347 (2009), no. 23-24, 1325--1330.

Mathematics

Number Theory

6 pages

Scientific paper

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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