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arXiv · 1612.07898

On component groups of Jacobians of quaternionic modular curves

Mihran Papikian
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Abstract

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 Livn\'e.

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Mihran Papikian. 2016-12-23. On component groups of Jacobians of quaternionic modular curves. https://doi.org/10.1007/s00013-016-0927-x

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