Mathematical Research Letters

Volume 25 (2018)

Number 3

On multiplicities of Galois representations in cohomology groups of Shimura curves

Pages: 759 – 782



Chuangxun Cheng (Department of Mathematics, Nanjing University, Nanjing, China)

Ji Fu (Department of Mathematics, Nanzhou College, Nanxian, China)


In this paper, we construct examples where the multiplicities of rank two Galois representations in the localized first cohomology groups of Shimura curves over totally real fields are greater than one. These examples generalize the result of Ribet for Jacobians of Shimura curves over $\mathbb{Q}$ and are closely related to the BDJ conjecture.


Shimura curves, Galois representations, $p$-adic uniformization

2010 Mathematics Subject Classification

11F80, 11G18

Received 26 June 2016

Accepted 2 March 2017

Published 3 August 2018