Shimura subgroups of Jacobians of Shimura curves
Date of Issue1993
School of Physical and Mathematical Sciences
Given an indefinite quaternion algebra of reduced discriminant D and an integer N relatively prime to D, one can construct Shimura curves Sh0(N, D) and Sh1(N, D), which are analogues of X0(N) and X1(N). The natural morphism Sh1(N, D) —>Sh0(N, D) induces a morphism J0(N, D) —>J1(N, D)between the Jacobians. We compute the kernel ∑(N, D) of this latter map, which is finite.
Proceedings of the American mathematical society
© 1993 American Mathematical Society This paper was published in [Proceedings of the American Mathematical Society] and is made available as an electronic reprint (preprint) with permission of [American Mathematical Society]. The paper can be found at DOI:http://dx.doi.org/10.1090/S0002-9939-1993-1145947-2. One print or electronic copy may be made for personal use only. Systematic or multiple reproduction, distribution to multiple locations via electronic or other means, duplication of any material in this paper for a fee or for commercial purposes, or modification of the content of the paper is prohibited and is subject to penalties under law.