Year: 2020
Type: article
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 $$\mathbb {Q}$$ 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.
Source: Mathematische Annalen
Authors: Jeffrey Manning, Jack Shotton
Institutions: University of California, Los Angeles, Durham University
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $2,750
Funder: Durham University
OpenAlex ID: W2960087631