Analogues of proper-smooth basechange for etale cohomology

Question

If we are given a map of schemes $f:X\to S$ that is smooth and proper the proper-smooth basechange Theorem will say that the derived functors the sheaf $R^if_*\mathbb{Q}_\ell$ is lcc. I was wondering if there are other situations in which we can also conclude that the these sheaves are "local systems". I am particularly interested in the situation in which $S=Spec(\mathbb{Z}_p)$, the map $f:X\to S$ is only assumed smooth and you want to want to conclude $H_c^i(X_{\over{\mathbb{F}}_p},\mathbb{Q}_\ell)=H_c^i(X_{\over{\mathbb{Q}}_p},\mathbb{Q}_\ell)$. What would we have to assume on the compactification? Any reference to a classically know case would be much appreciated.