### Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties

Kai-Wen Lan and Junecue Suh
Source: Duke Math. J. Volume 161, Number 6 (2012), 1113-1170.

#### Abstract

Given a compact PEL-type Shimura variety, a sufficiently regular weight (defined by mild and effective conditions), and a prime number $p$ unramified in the linear data and larger than an effective bound given by the weight, we show that the (Betti) cohomology with $\mathbb {Z}_{p}$-coefficients of the given weight vanishes away from the middle degree, and hence has no $p$-torsion. We do not need any other assumption (such as ones on the images of the associated Galois representations).

First Page:
Primary Subjects: 11G18
Secondary Subjects: 14F17, 14F30, 11F75
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Permanent link to this document: http://projecteuclid.org/euclid.dmj/1333633317
Digital Object Identifier: doi:10.1215/00127094-1548452
Zentralblatt MATH identifier: 06029039
Mathematical Reviews number (MathSciNet): MR2913102

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