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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.
We investigate the relation between p-adic Galois representations and overconvergent (phi,Gamma)-modules in families. Especially we construct a natural open subspace of a family of (phi,Gamma)-modules, over which it is induced by a family of Galois-representations.
We study the relation of the notion of weak admissibility in families of filtered phi-modules, as considered in a companion paper, with the adjoint quotient. We show that the weakly admissible subset is an open subvariety in the fibers over the adjoi
We apply the theory of families of (phi,Gamma)-modules to trianguline families as defined by Chenevier. This yields a new definition of Kisins finite slope subspace as well as higher dimensional analogues. Especially we show that these finite slope s
This paper contains three new results. {bf 1}.We introduce new notions of projective crystalline representations and twisted periodic Higgs-de Rham flows. These new notions generalize crystalline representations of etale fundamental groups introduced
Let $mathcal{X}$ be a regular projective arithmetic variety equipped with an ample hermitian line bundle $overline{mathcal{L}}$. We prove that the proportion of global sections $sigma$ with $leftlVert sigma rightrVert_{infty}<1$ of $overline{mathcal{