On component groups of Jacobians of quaternionic modular curves

Research output: Contribution to journalArticle

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

Original languageEnglish (US)
Pages (from-to)315-328
Number of pages14
JournalArchiv der Mathematik
Volume107
Issue number4
DOIs
StatePublished - Oct 1 2016

Fingerprint

Modular Curves
Quaternion Algebra
Finite Graph
Weighted Graph
Discriminant
Pairing
Deduce
Eigenvalue
Cycle

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

Cite this

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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 Fq(T) or Q. Our formula over Q recovers a result of Jordan and Livn{\'e}.",
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On component groups of Jacobians of quaternionic modular curves. / Papikian, Mihran.

In: Archiv der Mathematik, Vol. 107, No. 4, 01.10.2016, p. 315-328.

Research output: Contribution to journalArticle

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