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

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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.

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  1. DPMMS, Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge, CB3 0WA, UK

    James Newton

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  1. James Newton
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Newton, J. Completed cohomology of Shimura curves and a p-adic Jacquet–Langlands correspondence. Math. Ann. 355, 729–763 (2013). https://doi.org/10.1007/s00208-012-0796-y

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  • DOI: https://doi.org/10.1007/s00208-012-0796-y

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