On component groups of Jacobians of quaternionic modular curves

Mihran Papikian

doi:10.1007/s00013-016-0927-x

On component groups of Jacobians of quaternionic modular curves

Mihran Papikian

Mathematics

Research output: Contribution to journal › Article › peer-review

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 F_q(T) or Q. Our formula over Q recovers a result of Jordan and Livné.

Original language	English (US)
Pages (from-to)	315-328
Number of pages	14
Journal	Archiv der Mathematik
Volume	107
Issue number	4
DOIs	https://doi.org/10.1007/s00013-016-0927-x
State	Published - Oct 1 2016

All Science Journal Classification (ASJC) codes

General Mathematics

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10.1007/s00013-016-0927-x

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AB - 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 Fq(T) or Q. Our formula over Q recovers a result of Jordan and Livné.

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On component groups of Jacobians of quaternionic modular curves

Abstract

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