  Given a scheme X over a complete discrete valuation ring ${\mathcal O}_K$ of
mixed characteristic,Gros,in his study of syntomic cohomology in the smooth and
proper case, introduced a filtration on the rigid cohomology of the special
fiber $X_k$.Gros claimed that this construction was independent of the choice
of immersions involved, citing an unpublished paper of Berthelot. However no
proofs of this have appeared: here we prove it.
