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We study duality theorems for the relative logarithmic de Rham-Witt sheaveson semi-stable schemes $X$ over a local ring $\mathbb{F}_q[[t]]$, where$\mathbb{F}_q$ is a finite field. As an application, we obtain a new filtrationon the maximal abelian quotient $\pi^{\text{ab}}_1(U)$ of the \'etalefundamental groups $\pi_1(U)$ of an open subscheme $U \subseteq X$, which givesa measure of ramification along a divisor $D$ with normal crossing and$\text{Supp}(D) \subseteq X-U$. This filtration coincides with theBrylinski-Kato-Matsuda filtration in the relative dimension zero case.

Duality for relative logarithmic de Rham-Witt sheaves on semistable schemes over $\mathbb{F}_q[[t]]$