Parametrization of abelian $K$-surfaces with quaternionic multiplication
Number Theory
2010-03-25 v2 Algebraic Geometry
Abstract
We prove that the abelian -surfaces whose endomorphism algebra is a quaternion algebra are parametrized, up to isogeny, by the -rational points of the quotient of certain Shimura curves by the group of their Atkin-Lehner involutions.
Keywords
Cite
@article{arxiv.0906.2559,
title = {Parametrization of abelian $K$-surfaces with quaternionic multiplication},
author = {Xavier Guitart and Santiago Molina},
journal= {arXiv preprint arXiv:0906.2559},
year = {2010}
}
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6 pages