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.
Bibliographical noteFunding 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.
- Interior cohomology
- P-adic cohomology
- Shimura varieties
- Vanishing theorems