Patching and the completed homology of locally symmetric spaces
File(s)
Accepted version
Author(s)
Gee, Toby
Newton, James
Type
Working Paper
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).
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).
Date Issued
2019-11-18
Citation
2019
Publisher
arXiv
Copyright Statement
© 2019 The Author(s)
Sponsor
Engineering & Physical Science Research Council (EPSRC)
Commission of the European Communities
The Leverhulme Trust
Commission of the European Communities
Identifier
http://arxiv.org/abs/1609.06965v5
Grant Number
EP/L025485/1
FP7-ERC-StG-2012-306326
LH.PZ.GEE.2012
FP7-PEOPLE-2011-CIG-303605
Subjects
math.NT
math.NT
Notes
v2: an issue with the definition of the big Hecke algebra has been fixed. Some other minor changes. v3: slightly weakened the local--global compatibility Conjecture (Conjecture 5.1.12). v4: minor changes, mostly to introduction. v5: fixed an issue in Appendix B, some other minor changes
Publication Status
Published