  For a curve $C$ over a perfect field $k$ of characteristic $p > 0$ we study
the tame cohomology of $X = \textit{Spa}(C,k)$ introduced in arXiv:1801.04776.
We prove that the tame cohomology groups of $X$ with $p$-torsion coefficients
satisfy cohomological purity (which is not true in full generality for the
\'etale cohomology). Using purity we show Poincar\'e duality for the tame
cohomology of $X$ with $p$-torsion coefficients.
