Weight-monodromy conjecture over equal characteristic local fields

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.