Duke Mathematical Journal
- Duke Math. J.
- Volume 161, Number 6 (2012), 1113-1170.
Vanishing theorems for torsion automorphic sheaves on compact PEL-type Shimura varieties
Given a compact PEL-type Shimura variety, a sufficiently regular weight (defined by mild and effective conditions), and a prime number unramified in the linear data and larger than an effective bound given by the weight, we show that the (Betti) cohomology with -coefficients of the given weight vanishes away from the middle degree, and hence has no -torsion. We do not need any other assumption (such as ones on the images of the associated Galois representations).
Duke Math. J., Volume 161, Number 6 (2012), 1113-1170.
First available in Project Euclid: 5 April 2012
Permanent link to this document
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
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
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