Mathematical Research Letters

Volume 25 (2018)

Number 3

On multiplicities of Galois representations in cohomology groups of Shimura curves

Pages: 759 – 782

DOI: http://dx.doi.org/10.4310/MRL.2018.v25.n3.a2

Authors

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

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

Abstract

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.

Keywords

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

2010 Mathematics Subject Classification

11F80, 11G18

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Received 26 June 2016