We construct a functor from the category of p-adic étale local systems on a smooth rigid analytic variety X over a p-adic field to the category of vector bundles with an integrable connection on its "base change to B dR ", which can be regarded as a first step towards the sought-after p-adic RiemannHilbert correspondence. As a consequence, we obtain the following rigidity theorem for p-adic local systems on a connected rigid analytic variety: if the stalk of such a local system at one point, regarded as a p-adic Galois representation, is de Rham in the sense of Fontaine, then the stalk at every point is de Rham. Along the way, we also establish some basic properties of the p-adic Simpson correspondence. Finally, we give an application of our results to Shimura varieties. R.

Given a p-adic representation of the Galois group of a local field, we show that its Galois cohomology can be computed using the associatedétale (ϕ, Γ)-module over the Robba ring; this is a variant of a result of Herr. We then establish analogues, for not necessarilyétale (ϕ, Γ)-modules over the Robba ring, of the Euler-Poincaré characteristic formula and Tate local duality for p-adic representations. These results are expected to intervene in the duality theory for Selmer groups associated to de Rham representations.

A simple and versatile probe was discovered for discriminating between different thiol species with the use of CTAB (cetyl trimethylammonium bromide).

We prove the global triangulation conjecture for families of refined p-adic representations under a mild condition. That is, for a refined family, the associated family of (ϕ, Γ)-modules admits a global triangulation on a Zariski open and dense subspace of the base that contains all regular non-critical points. We also determine a large class of points which belongs to the locus of global triangulation. Furthermore, we prove that all the specializations of a refined family are trianguline. In the case of the Coleman-Mazur eigencurve, our results provide the key ingredient for showing its properness in a subsequent work [15]. Definition 1.2.1. For any s ≥ s 0 , define the presheaves D †,s rig,K (V S ) and D † rig,K (V S ) on the weak G-topology of M (S) by setting D †,s rig,K (V S )(M (S )) = D †,s rig,K (V S ), D † rig,K (V S )(M (S )) = D † rig,K (V S ) for any affinoid subdomain M (S ) of M (S).