On component groups of Jacobians of quaternionic modular curves

摘要

We use a combinatorial result relating the discriminant of the cycle pairing on a weighted finite graph to the eigenvalues of its Laplacian to deduce a formula for the orders of component groups of Jacobians of modular curves arising from quaternion algebras over F-q(T) or Q. Our formula over Q recovers a result of Jordan and Livne.