Beilinson's results (two papers, one mentioned by Keerthi and [the other here][1]) have been generalised by Bhargav Bhatt; [his paper][2] also introduces a global period ring $A_{ddR}$ for global Galois representations!! The ring $A_{ddR}$ is a filtered $\hat{Z}$-algebra equipped with a Gal$(\bar{Q}/{Q})$-action. 

A (one of the many) beautiful result in this paper is the following theorem:

Let $X$ be a semistable variety over $Q$. Then the log de Rham cohomology of a semistable model for $X$ is isomorphic to the $\hat{Z}$-etale cohomology of $X_{\bar{Q}}$, once both sides are base changed to a localization of $A_{ddR}$ (whle preserving all natural structures on either side).


  [1]: http://arxiv.org/abs/1111.3316
  [2]: http://math.uchicago.edu/~drinfeld/p-adic_periods/Bhatt-p-adic_derived_de_Rham.pdf