Patching and the completed homology of locally symmetric spaces

Toby Gee; James Newton

doi:10.1017/s1474748020000158

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arXiv · 1609.06965

Patching and the completed homology of locally symmetric spaces

Toby Gee·James Newton

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Abstract

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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Toby Gee, James Newton. 2016-09-22. Patching and the completed homology of locally symmetric spaces. https://doi.org/10.1017/s1474748020000158

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