On maps between modular Jacobians and Jacobians of Shimura curves

摘要

Fix a squarefree integer N, divisible by an even number of primes, and let Γ′ be a congruence subgroup of level M, where M is prime to N. For each D dividing N and divisible by an even number of primes, the Shimura curve X D (Γ0(N/D) ∩ Γ′) associated to the indefinite quaternion algebra of discriminant D and Γ0(N/D) ∩ Γ′-level structure is well defined, and we can consider its Jacobian J D (Γ0(N/D) ∩ Γ′). Let J D denote the N/D-new subvariety of this Jacobian.