A ring $R$ is called excellent if is quasi-excellent (so is a G-ring and a J-2 ring) and universally catenary.
Following two questions:
1) Wiki says that excellent ring "behave well with respect to the completion" $R \to \hat{R}$.
What does this mean concretely? Is there a wide class of properties properties P such that one have
"$R$ has property P $\Rightarrow \hat{R}$ has also property P"?
If yes, which properties P are meant? Which arguments can be done working with excellent rings? Or has "behave well with respect to the completion" another meaning?
2) Is there any geometric intuition (in sense of corresponding top space $Spec(R)$ behind excellent rings?