I am looking for a functor from varieties $X/\mathbf{Z}_p$ to $(\varphi,\Gamma)$modules over the Robba ring over $\mathbf{Q}_p$ (overconvergent ones) that is contructed by differential methods (similar to logcrystaline cohomology) not by Galois methods and a twist by a Fontaine ring (would like to avoid, if possible, the use of the field of norms).
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