Abstract
In this paper, as a generalization of Berger's construction, we give a functor from the category of families of filtered (ϕ, N )-modules (with certain condition) to the category of families of (ϕ, Γ)-modules. Combining this with Kedlaya and Liu's theorem we show that, when the base is a reduced affinoid space, every family of weakly admis- sible filtered (ϕ, N )-modules can locally be converted into a family of semistable Galois representations.
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