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

de Vera-Piquero, Carlos

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

Idioma: Inglés

DOI: 10.1016/j.jnt.2013.04.018

Año: 2013

Publicado en: JOURNAL OF NUMBER THEORY 133, 10 (2013), 3500-3516
ISSN: 0022-314X

Factor impacto JCR: 0.524 (2013)

Categ. JCR: MATHEMATICS rank: 176 / 301 = 0.585 (2013) - Q3 - T2

Tipo y forma: Article (PostPrint)