Weight-monodromy conjecture over equal characteristic local fields
Tetsushi Ito
Abstract
The aim of this paper is to study certain properties of the weight spectral sequences of Rapoport-Zink by a specialization argument. By reducing to the case over finite fields previously treated by Deligne, we prove that the weight filtration and the monodromy filtration defined on the l-adic étale cohomology coincide, up to shift, for proper smooth varieties over equal characteristic local fields. We also prove that the weight spectral sequences degenerate at E2 in any characteristic without using log geometry. Moreover, as an application, we give a modulo p>0 reduction proof of a Hodge analogue previously considered by Steenbrink.
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