Patching and the completed homology of locally symmetric spaces
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 with GLn over a number field. We use our construction, and some new results in non-commutative al...
| Auteurs principaux: | , |
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| Format: | Journal article |
| Langue: | English |
| Publié: |
Cambridge University Press
2020
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| Résumé: | 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 with GLn over a number field. We use our construction, and some new results in non-commutative algebra, to show that standard conjectures on completed homology imply ‘big R=big T ’ theorems in situations where one cannot hope to appeal to the Zariski density of classical points (in contrast to all previous results of this kind). In the case where n=2 and p splits completely in the number field, we relate our construction to the p -adic local Langlands correspondence for GL2(Qp) . |
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