The Kernel of Ribet’s Isogeny for Genus Three Shimura Curves
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چکیده
There are exactly nine reduced discriminants D of indefinite quaternion algebras over Q for which the Shimura curve XD attached to D has genus 3. We present equations for these nine curves and, moreover, for each D we determine a subgroup c(D) of cuspidal divisors of degree zero of Jac(X0(D)) such that the abelian variety Jac(X0(D))/c(D) is the jacobian of the curve XD.
منابع مشابه
Equations of Shimura Curves of Genus
We present explicit models for Shimura curves X D and Atkin-Lehner quotients X D /ωm of them of genus 2. We show that several equations conjectured by Kurihara are correct and compute for them the kernel of Ribet's isogeny J 0 (D) new → J D between the new part of the Jacobian of the modular curve X 0 (D) and the Jacobian of X D .
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تاریخ انتشار 2014