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

Kai Wen Lan, Junecue Suh

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19 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 languageEnglish (US)
Pages (from-to)228-286
Number of pages59
JournalAdvances in Mathematics
Volume242
DOIs
StatePublished - 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

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