Journal article

### Shimura varieties at level $\Gamma_1(p^{\infty})$ and Galois representations

Abstract:

We show that the compactly supported cohomology of certain U(n, n) or Sp(2n)-Shimura varieties with Γ1(p∞)-level vanishes above the middle degree. The only assumption is that we work over a CM field F in which the prime p splits completely. We also give an application to Galois representations for torsion in the cohomology of the locally symmetric spaces for GLn/F. More precisely, we use the vanishing result for Shimura varieties to eliminate the nilpotent ideal in the construction of these G...

Publication status:
Published
Peer review status:
Peer reviewed

### Access Document

Files:
Publisher copy:
10.1112/S0010437X20007149

### Authors

More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Subgroup:
Mathematical Institute
Role:
Author
ORCID:
0000-0002-6825-0458
More by this author
Institution:
University of Oxford
Division:
MPLS
Department:
Mathematical Institute
Subgroup:
Mathematical Institute
Role:
Author
Publisher:
Cambridge University Press Publisher's website
Journal:
Compositio Mathematica Journal website
Volume:
156
Issue:
6
Pages:
1152-1230
Publication date:
2020-05-26
Acceptance date:
2020-02-06
DOI:
EISSN:
1570-5846
ISSN:
0010-437X
Pubs id:
1088180
Local pid:
pubs:1088180
Language:
English
Keywords: