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I have a question on p-adic Hodge theory: When e.g. $X$ is a smooth proper scheme over a finite extension $K$ of $\mathbf{Q}_{p}$ then e.g. one variant of $p$-adic Hodge theory says that there is a ...

Let $K$ be a finite extension of $\mathbb{Q}_p$, and let $C=\widehat{\overline{K}}$ be the completion of the algebraic closure of $K$. Let $\mathscr{O}_C$ be the ring of integers in $C$, and let $G_K$ ...

Notation is as in the question: https://math.stackexchange.com/questions/4090045/some-questions-about-the-robba-ring. We define a new operator over the Robba ring as follows. Put $$c=\frac{pE(u)}{E(0)}...