On Families of (',) -modules

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Relative P-adic Hodge Theory: Foundations (2013, background): “However, this functor is not an equivalence of categories; rather, it can only be inverted locally [28], [74].”
Triangulation of refined families (2012, background): “cks respectively. That is, the natural morphisms ’(Dy K (V S)) !D y K (V S) and ’(Dy rig;K (V S)) !D y rig;K (V S) are isomorphisms. Thus D y K (V S) is a (’;)-module over By K b Q p Sin the sense of [23]. (See Remark 4.2.8 for the relevant discussion about D y rig;K (V S).) Remark 1.1.6. In the cas”
Cohomology of arithmetic families of (,Γ)-modules (2012, methodology): “Another complication is that the theory of slope filtrations does not extend in a completely satisfactory way to families; see [34] for discussion of some of the difficulties.”