PATCHING and the COMPLETED HOMOLOGY of LOCALLY SYMMETRIC SPACES

Author: 

Gee, T
Newton, J

Publication Date: 

27 May 2020

Journal: 

Journal of the Institute of Mathematics of Jussieu

Last Updated: 

2021-11-28T17:28:50.233+00:00

DOI: 

10.1017/S1474748020000158

abstract: 

Under an assumption on the existence of -adic Galois representations, we carry out Taylor-Wiles patching (in the derived category) for the completed homology of the locally symmetric spaces associated with 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 ' 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 and splits completely in the number field, we relate our construction to the -adic local Langlands correspondence for.

Symplectic id: 

1193795

Submitted to ORA: 

Submitted

Publication Type: 

Journal Article