Abstract
Let X D 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 X D , Jordan and Skorobogatov introduced a covering X D , p of X D whose maximal étale quotient is referred to as the Shimura covering of X D at p . The goal of this note is to describe the group of modular automorphisms of the curve X D , p and its quotients. As an application, we construct cyclic étale Galois coverings of Atkin–Lehner quotients of X D .
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