- 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...
Expand abstract - Publication status:
- Published
- Peer review status:
- Peer reviewed
- Files:
-
- Publisher copy:
- 10.1112/S0010437X20007149
-
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- 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:
- Copyright holder:
- Caraiani et al.
- Copyright date:
- 2020
- Rights statement:
- © The Authors 2020
- Notes:
- This is the accepted manuscript version of the article. The final version is available from Cambridge University Press at: https://doi.org/10.1112/S0010437X20007149
Journal article
Shimura varieties at level $\Gamma_1(p^{\infty})$ and Galois representations
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