On the group of automorphisms of Shimura curves and applications

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Let V_D be the Shimura curve over \Q attached to the indefinite rational quaternion algebra of discriminant D. In this note we investigate the group of automorphisms of V_D and prove that, in many cases, it is the Atkin-Lehner group. Moreover, we determine the family of bielliptic Shimura curves over \bar \Q and over \Q and we use it to study the set of rational points on V_D over quadratic fields. Finally, we obtain explicit equations of elliptic Atkin-Lehner quotients of V_D.
To appear in Compositio Mathematica

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Algebraic Geometry, Number Theory, 11G18;14G35

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http://salesiana.dossiersoluciones.com/handle/123456789/64270

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0206101
 http://arxiv.org/abs/math/0206101

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arXiv