On component groups of Jacobians of quaternionic modular curves

被引：0

作者：

Papikian, Mihran ^{[1
,2
]}

机构：

[1] Penn State Univ, Dept Math, University Pk, PA 16802 USA

[2] Max Planck Inst Math, Vivatsgasse 7, D-53111 Bonn, Germany

来源：

ARCHIV DER MATHEMATIK | 2016年 / 107卷 / 04期

关键词：

Graph Laplacian; Component group; Shimura curve; JACQUET-LANGLANDS ISOGENY; EIGENVALUES;

D O I：

10.1007/s00013-016-0927-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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 Livne.

引用

页码：315 / 328

页数：14

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