The Shimura covering of a Shimura curve: automorphisms and étale subcoverings

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Title:	The Shimura covering of a Shimura curve: automorphisms and étale subcoverings
Author:	Vera Piquero, Carlos de
Abstract:	Let XDXD be the Shimura curve associated with an indefinite rational quaternion algebra of discriminant D, and let p be a prime dividing D. In their investigations on the arithmetic of XD, Jordan and Skorobogatov introduced a covering XD,pXD,p of XD whose maximal étale quotient is referred to as the Shimura covering of XD at p. The goal of this note is to describe the group of modular automorphisms of the curve XD,pXD,p and its quotients. As an application, we construct cyclic étale Galois coverings of Atkin–Lehner quotients of XD.
Abstract:	Peer Reviewed
Subject(s):	-Atkin-Lehner quotients -Étale coverings -Modular automorphisms -Shimura curves -Classificació AMS::11 Number theory::11G Arithmetic algebraic geometry (Diophantine geometry) -Classificació AMS::14 Algebraic geometry::14G Arithmetic problems. Diophantine geometry
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Document type:	Article - Published version Article
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