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Patching and the completed homology of locally symmetric spaces
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Under an assumption on the existence of p-adic Galois representations, we carry out Taylor--Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated to GL(n) over a number field. We use our construction to show that standard conjectures on completed homology imply `big R = big T' theorems. In the case that n=2 and p splits completely in the number field, we relate our construction to the p-adic local Langlands correspondence for GL(2,Q_p).
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Cited by 1 Pith paper
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On the modularity of 2-adic potentially semi-stable deformation rings
For p=2, the support of patched modules meets every irreducible component of the potentially semi-stable deformation ring, yielding the Breuil-Mezard conjecture in the case where the residual representation is a twist...
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