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

Manning, Jeffrey and Shotton, Jack (2021) 'Ihara’s Lemma for Shimura curves over totally real fields via patching.', Mathematische annalen., 379 . pp. 187-234.


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.

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Date accepted:No date available
Date deposited:05 October 2020
Date of first online publication:25 September 2020
Date first made open access:05 October 2020

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