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

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

2011-07-05

arxiv.org/abs/1107.0923v1

Mathematics

Number Theory

24 pages

Scientific paper

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.

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