Contents Online
Mathematical Research Letters
Volume 25 (2018)
Number 3
On multiplicities of Galois representations in cohomology groups of Shimura curves
Pages: 759 – 782
DOI: https://dx.doi.org/10.4310/MRL.2018.v25.n3.a2
Authors
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
Received 26 June 2016
Accepted 2 March 2017
Published 3 August 2018