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Weight-monodromy conjecture for p-adically uniformized varieties

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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.

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  1. Department of Mathematics, Faculty of Science, Kyoto University, Kyoto, 606-8502, Japan

    Tetsushi Ito

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Ito, T. Weight-monodromy conjecture for p-adically uniformized varieties. Invent. math. 159, 607–656 (2005). https://doi.org/10.1007/s00222-004-0395-y

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