On component groups of Jacobians of quaternionic modular curves

preprint2016arXivOpen access

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 $\mathbb{F}_q(T)$ or $\mathbb{Q}$ . Our formula over $\mathbb{Q}$ recovers a result of Jordan and Livné.

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On component groups of Jacobians of quaternionic modular curves

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