15 April 2012 Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties
Kai-Wen Lan, Junecue Suh
Duke Math. J. 161(6): 1113-1170 (15 April 2012). DOI: 10.1215/00127094-1548452

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 Zp-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).

Citation

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Kai-Wen Lan. Junecue Suh. "Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties." Duke Math. J. 161 (6) 1113 - 1170, 15 April 2012. https://doi.org/10.1215/00127094-1548452

Information

Published: 15 April 2012
First available in Project Euclid: 5 April 2012

zbMATH: 1296.11072
MathSciNet: MR2913102
Digital Object Identifier: 10.1215/00127094-1548452

Subjects:
Primary: 11G18
Secondary: 11F75 , 14F17 , 14F30

Rights: Copyright © 2012 Duke University Press

Vol.161 • No. 6 • 15 April 2012
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