Weight-monodromy conjecture for p-adically uniformized varieties
Abstract
The aim of this paper is to prove the weight-monodromy conjecture (Deligne's conjecture on the purity of monodromy filtration) for varieties p-adically uniformized by the Drinfeld upper half spaces of any dimension. The ingredients of the proof are to prove a special case of the Hodge standard conjecture, and apply a positivity argument of Steenbrink, M. Saito to the weight spectral sequence of Rapoport-Zink. As an application, by combining our results with the results of Schneider-Stuhler, we compute the local zeta functions of p-adically uniformized varieties in terms of representation theoretic invariants. We also consider a p-adic analogue by using the weight spectral sequence of Mokrane.
Cite
@article{arxiv.math/0301201,
title = {Weight-monodromy conjecture for p-adically uniformized varieties},
author = {Tetsushi Ito},
journal= {arXiv preprint arXiv:math/0301201},
year = {2009}
}
Comments
47 pages, minor modifications, Section 7 (Appendix, application to the Tate conjecture) added, to appear in Inventiones mathematicae