Completed cohomology of Shimura curves and a p-adic Jacquet-Langlands correspondence

Abstract

We study indefinite quaternion algebras over totally real fields F, and give an example of a cohomological construction of p-adic Jacquet-Langlands functoriality using completed cohomology. We also study the (tame) levels of p-adic automorphic forms on these quaternion algebras and give an analogue of Mazur's `level lowering' principle.

Updated version. Contains some minor corrections compared to the published version

References in corpus (3)

• On Serre's conjecture for mod l Galois representations over totally real fields
• Hilbert modular forms and p-adic Hodge theory
• Geometric level raising for p-adic automorphic forms

Cited by in corpus (6)

• The Jacquet-Langlands correspondence for overconvergent Hilbert modular forms
• Infinitesimal characters in arithmetic families
• Towards local-global compatibility for Hilbert modular forms of low weight
• $\mathcal{L}$-invariants, partially de Rham families and local-global compatibility
• $\mathcal{L}$-invariants and local-global compatibility for the group ${\mathrm{GL}}_2/F$
• A p-adic Labesse-Langlands transfer