We consider stacks of filtered phi-modules over rigid analytic spaces and
adic spaces. We show that these modules parametrize p-adic Galois
representations of the absolute Galois group of a p-adic field with varying
coefficients over an open substack containing all classical points. Further we
study a period morphism (defined by Pappas and Rapoport) from a stack
parametrizing integral data and determine the image of this morphism.Comment: 52 pages. More details in the last section. One of the section has
become a paper of its ow
