Weight-monodromy conjecture for p-adically uniformized varieties

Details Weight-monodromy conjecture for p-adically uniformized varieties Weight-monodromy conjecture for p-adically uniformized varieties

2003-01-20

arxiv.org/abs/math/0301201v3

Mathematics

Number Theory

47 pages, minor modifications, Section 7 (Appendix, application to the Tate conjecture) added, to appear in Inventiones mathem

Scientific paper

10.1007/s00222-004-0395-y

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.

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