Author
Caraiani, A
Gulotta, D
Hsu, C
Johansson, H
Mocz, L
Reinecke, E
Shih, S
Journal title
Compositio Mathematica
DOI
10.1112/S0010437X20007149
Issue
6
Volume
156
Last updated
2021-07-25T22:19:51.143+01:00
Page
1152-1230
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 Galois representations. This
strengthens recent results of Scholze [Sch15] and Newton-Thorne [NT16].
Symplectic ID
1088180
Publication type
Journal Article
Publication date
26 May 2020
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