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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


Jeffrey Manning


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.

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
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Published Journal Article (Advance online version) (651 Kb)

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