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Patching and the completed homology of locally symmetric spaces

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 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...

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Publication status:
Published
Peer review status:
Peer reviewed

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Publisher copy:
10.1017/S1474748020000158

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Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Oxford college:
Merton College
Role:
Author
ORCID:
0000-0002-9332-5204
Publisher:
Cambridge University Press Publisher's website
Journal:
Journal of the Institute of Mathematics of Jussieu Journal website
Publication date:
2020-05-27
Acceptance date:
2020-03-11
DOI:
EISSN:
1475-3030
ISSN:
1474-7480
Pubs id:
1193795
Local pid:
pubs:1193795

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