On the group of automorphisms of Shimura curves and applications

Simple item page
dc.creatorRotger, Victor
dc.date2002-06-10
dc.date.accessioned2026-07-07T04:49:01Z
dc.date.available2026-07-07T04:49:01Z
dc.descriptionLet 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.
dc.descriptionTo appear in Compositio Mathematica
dc.identifierhttps://arxiv.org/abs/math/0206101
dc.identifierhttp://arxiv.org/abs/math/0206101
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/64270
dc.subjectAlgebraic Geometry
dc.subjectNumber Theory
dc.subject11G18;14G35
dc.titleOn the group of automorphisms of Shimura curves and applications
dc.typetext

Files

Collections

arXiv