On component groups of Jacobians of quaternionic modular curves

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...

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Bibliographic Details
Published in:Archiv der Mathematik 2016-10, Vol.107 (4), p.315-328
Main Author: Papikian, Mihran
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Quaternions
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Summary: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 Livné.
ISSN:0003-889X
1420-8938
DOI:10.1007/s00013-016-0927-x