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Shimura subgroups of Jacobians of Shimura curves

Author: San Ling
Journal: Proc. Amer. Math. Soc. 118 (1993), 385-390
MSC: Primary 11G18; Secondary 14G35, 14H40
MathSciNet review: 1145947
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Abstract: Given an indefinite quaternion algebra of reduced discriminant $ D$ and an integer $ N$ relatively prime to $ D$, one can construct Shimura curves $ {\operatorname{Sh} _0}(N,D)$ and $ {\operatorname{Sh} _1}(N,D)$, which are analogues of $ {X_0}(N)$ and $ {X_1}(N)$. The natural morphism $ {\operatorname{Sh} _1}(N,D) \to {\operatorname{Sh} _0}(N,D)$ induces a morphism $ {J_0}(N,D) \to {J_1}(N,D)$ between the Jacobians. We compute the kernel $ \sum (N,D)$ of this latter map, which is finite.

References [Enhancements On Off] (What's this?)

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Article copyright: © Copyright 1993 American Mathematical Society

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