So let $R$ be a discrete valuation ring and let $X$ be a scheme which is proper and flat over $R$. Let $X\_s$ denote the special fiber of $X$. 

So intuitively, when somebody says that a curve $X$ is semistable I kind of equate this in my mind with the property that $X\_s$ has only ordinary double points as singularities.

**Q1**: So in general (i.e. in higher dimension) what is the geometrical meaning for a scheme
to be semistable? 

On the Galois representation side we have a very precise definition of what semistable means using Fontaine's ring $\mathbf{B}\_{st}$. 

**Q2** If there is a precise answer to **Q1**, is there a good reference (more on the intuitive side than on the technical side) where one shows the equivalence (under suitable assumptions) that the geometrical definition coincides with the galois representation one?