Duke Mathematical Journal

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

Kai-Wen Lan and Junecue Suh

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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).

Article information

Source
Duke Math. J., Volume 161, Number 6 (2012), 1113-1170.

Dates
First available in Project Euclid: 5 April 2012

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1333633317

Digital Object Identifier
doi:10.1215/00127094-1548452

Mathematical Reviews number (MathSciNet)
MR2913102

Zentralblatt MATH identifier
1296.11072

Subjects
Primary: 11G18: Arithmetic aspects of modular and Shimura varieties [See also 14G35]
Secondary: 14F17: Vanishing theorems [See also 32L20] 14F30: $p$-adic cohomology, crystalline cohomology 11F75: Cohomology of arithmetic groups

Citation

Lan, Kai-Wen; Suh, Junecue. Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties. Duke Math. J. 161 (2012), no. 6, 1113--1170. doi:10.1215/00127094-1548452. https://projecteuclid.org/euclid.dmj/1333633317


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