Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ihara's lemma for Shimura curves over totally real fields via patching   We prove Ihara's lemma for the mod $l$ cohomology of Shimura curves,
localised 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 $\mathbb{Q}$, 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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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: gr-qc
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The categories of this paper are: cmp-lg
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The categories of this paper are: stat
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The categories of this paper are: atom-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: q-alg
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The categories of this paper are: q-fin
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: adap-org
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The categories of this paper are: nlin
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The categories of this paper are: q-bio
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The categories of this paper are: mtrl-th