Potential semi-stability ofp-adic étale cohomology

We extend the methods of Faltings and Tsuji, and prove that ifK is a field of characteristic 0 with a complete, discrete valuation, and a perfect residue field of characteristicp, then thep-adic étale cohomology of a finite typeK-scheme is potentially semi-stable. We prove a similar result for cohomology with compact support, and for cohomology with support in a closed subspace ofX. We establish a relationship between these cohomology groups, and the de Rham cohomology ofX.