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

Kai Wen Lan; Junecue Suh

doi:10.1016/j.aim.2013.04.004

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

Kai Wen Lan, Junecue Suh

School of Mathematics

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We consider the interior cohomology (and the Hodge graded pieces in the case of the de Rham realization) of general-not necessarily compact-PEL-type Shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group. For primes p bigger than an effective bound, we prove that the Fp- and Zp-cohomology groups are concentrated in the middle degree, that the Zp-cohomology groups are free of p-torsion, and that every Fp-cohomology class lifts to a Zp-cohomology class.

Original language	English (US)
Pages (from-to)	228-286
Number of pages	59
Journal	Advances in Mathematics
Volume	242
DOIs	https://doi.org/10.1016/j.aim.2013.04.004
State	Published - Aug 1 2013

Bibliographical note

Funding Information:
The first author was supported by the Qiu Shi Science and Technology Foundation , and by the National Science Foundation under agreement Nos. DMS-0635607 and DMS-1069154. The second author was supported by the National Science Foundation under agreement No. DMS-0635607.

Keywords

Interior cohomology
Liftability
P-adic cohomology
Shimura varieties
Torsion-freeness
Vanishing theorems

Publisher link

10.1016/j.aim.2013.04.004

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title = "Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties",

abstract = "We consider the interior cohomology (and the Hodge graded pieces in the case of the de Rham realization) of general-not necessarily compact-PEL-type Shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group. For primes p bigger than an effective bound, we prove that the Fp- and Zp-cohomology groups are concentrated in the middle degree, that the Zp-cohomology groups are free of p-torsion, and that every Fp-cohomology class lifts to a Zp-cohomology class.",

keywords = "Interior cohomology, Liftability, P-adic cohomology, Shimura varieties, Torsion-freeness, Vanishing theorems",

author = "Lan, \{Kai Wen\} and Junecue Suh",

note = "Funding Information: The first author was supported by the Qiu Shi Science and Technology Foundation , and by the National Science Foundation under agreement Nos. DMS-0635607 and DMS-1069154. The second author was supported by the National Science Foundation under agreement No. DMS-0635607. ",

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T1 - Vanishing theorems for torsion automorphic sheaves on general PEL-type Shimura varieties

AU - Lan, Kai Wen

AU - Suh, Junecue

N1 - Funding Information: The first author was supported by the Qiu Shi Science and Technology Foundation , and by the National Science Foundation under agreement Nos. DMS-0635607 and DMS-1069154. The second author was supported by the National Science Foundation under agreement No. DMS-0635607.

PY - 2013/8/1

Y1 - 2013/8/1

N2 - We consider the interior cohomology (and the Hodge graded pieces in the case of the de Rham realization) of general-not necessarily compact-PEL-type Shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group. For primes p bigger than an effective bound, we prove that the Fp- and Zp-cohomology groups are concentrated in the middle degree, that the Zp-cohomology groups are free of p-torsion, and that every Fp-cohomology class lifts to a Zp-cohomology class.

AB - We consider the interior cohomology (and the Hodge graded pieces in the case of the de Rham realization) of general-not necessarily compact-PEL-type Shimura varieties with coefficients in the local systems corresponding to sufficiently regular algebraic representations of the associated reductive group. For primes p bigger than an effective bound, we prove that the Fp- and Zp-cohomology groups are concentrated in the middle degree, that the Zp-cohomology groups are free of p-torsion, and that every Fp-cohomology class lifts to a Zp-cohomology class.

KW - Interior cohomology

KW - Liftability

KW - P-adic cohomology

KW - Shimura varieties

KW - Torsion-freeness

KW - Vanishing theorems

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EP - 286

JO - Advances in Mathematics

JF - Advances in Mathematics

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

Abstract

Bibliographical note

Keywords

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