The kernel of Ribet's isogeny for genus three Shimura curves

抄録

There are exactly nine reduced discriminants D of indefinite quaternion algebras over ℚ for which the Shimura curve X_D 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))^new such that the abelian variety Jac(X₀(D))^new/c(D) is the jacobian of the curve X_D.