Universitat de Barcelona
2023-02-09T10:49:38Z
2023-02-09T10:49:38Z
2009-12
2023-02-09T10:49:38Z
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.
Article
Accepted version
English
Geometria algebraica aritmètica; Varietats abelianes; Arithmetical algebraic geometry; Abelian varieties
Elsevier Masson
Versió postprint del document publicat a: https://doi.org/10.1016/j.crma.2009.09.025
Comptes Rendus Mathématique , 2009, vol. 347, num. 23-24, p. 1325-1330
https://doi.org/10.1016/j.crma.2009.09.025
(c) Académie des Sciences ; French Academy of Sciences, 2009
