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Ihara’s Lemma for Shimura curves over totally real fields via patching

Manning, Jeffrey; Shotton, Jack

Ihara’s Lemma for Shimura curves over totally real fields via patching Thumbnail


Authors

Jeffrey Manning



Abstract

We prove Ihara’s lemma for the mod l cohomology of Shimura curves, localized at a maximal ideal of the Hecke algebra, under a large image hypothesis on the associated Galois representation. This was proved by Diamond and Taylor, for Shimura curves over Q, under various assumptions on l. Our method is totally different and can avoid these assumptions, at the cost of imposing the large image hypothesis. It uses the Taylor–Wiles method, as improved by Diamond and Kisin, and the geometry of integral models of Shimura curves at an auxiliary prime.

Citation

Manning, J., & Shotton, J. (2021). Ihara’s Lemma for Shimura curves over totally real fields via patching. Mathematische Annalen, 379, 187-234. https://doi.org/10.1007/s00208-020-02048-8

Journal Article Type Article
Online Publication Date Sep 25, 2020
Publication Date 2021-02
Deposit Date Oct 5, 2020
Publicly Available Date Oct 5, 2020
Journal Mathematische Annalen
Print ISSN 0025-5831
Electronic ISSN 1432-1807
Publisher Springer
Peer Reviewed Peer Reviewed
Volume 379
Pages 187-234
DOI https://doi.org/10.1007/s00208-020-02048-8
Public URL https://durham-repository.worktribe.com/output/1255064

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http://creativecommons.org/licenses/by/4.0/

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Advance online version This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.





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