Shimura subgroups of Jacobians of Shimura curves
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 th...
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| Format: | Article |
| Language: | English |
| Published: |
2012
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| Online Access: | https://hdl.handle.net/10356/79658 http://hdl.handle.net/10220/7621 |
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| Institution: | Nanyang Technological University |
| Language: | English |
| Summary: | 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. |
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